Question 24220: One Convolution Degree Is Not the Whole Exponential Addition Proof

Original question and givens

Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use x=20/21, y=-21/22, declared degree=19. Give (x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate).

• G001 — Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use x=20/21, y=-21/22, declared degree=19. Give (x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-real-exponential-function

Step-by-step derivation

source roles = [exp-addition-convolution]

derived = [[x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate]]

(20/21)^0

Exp convolution x power0 = 1

(-21/22)^19

Exp convolution y power19 = -13248496640331026125580781/32064977213018365645815808

Exp convolution numerator0 := mul(1, -13248496640331026125580781/32064977213018365645815808)

Exp convolution numerator0 = -13248496640331026125580781/32064977213018365645815808

source roles = [0]

derived = [1]

Exp convolution right0 factorial step1 := mul(1, 1)

Exp convolution right0 factorial step1 = 1

Exp convolution right0 factorial step2 := mul(1, 2)

Exp convolution right0 factorial step2 = 2

Exp convolution right0 factorial step3 := mul(2, 3)

Exp convolution right0 factorial step3 = 6

Exp convolution right0 factorial step4 := mul(6, 4)

Exp convolution right0 factorial step4 = 24

Exp convolution right0 factorial step5 := mul(24, 5)

Exp convolution right0 factorial step5 = 120

Exp convolution right0 factorial step6 := mul(120, 6)

Exp convolution right0 factorial step6 = 720

Exp convolution right0 factorial step7 := mul(720, 7)

Exp convolution right0 factorial step7 = 5040

Exp convolution right0 factorial step8 := mul(5040, 8)

Exp convolution right0 factorial step8 = 40320

Exp convolution right0 factorial step9 := mul(40320, 9)

Exp convolution right0 factorial step9 = 362880

Exp convolution right0 factorial step10 := mul(362880, 10)

Exp convolution right0 factorial step10 = 3628800

Exp convolution right0 factorial step11 := mul(3628800, 11)

Exp convolution right0 factorial step11 = 39916800

Exp convolution right0 factorial step12 := mul(39916800, 12)

Exp convolution right0 factorial step12 = 479001600

Exp convolution right0 factorial step13 := mul(479001600, 13)

Exp convolution right0 factorial step13 = 6227020800

Exp convolution right0 factorial step14 := mul(6227020800, 14)

Exp convolution right0 factorial step14 = 87178291200

Exp convolution right0 factorial step15 := mul(87178291200, 15)

Exp convolution right0 factorial step15 = 1307674368000

Exp convolution right0 factorial step16 := mul(1307674368000, 16)

Exp convolution right0 factorial step16 = 20922789888000

Exp convolution right0 factorial step17 := mul(20922789888000, 17)

Exp convolution right0 factorial step17 = 355687428096000

Exp convolution right0 factorial step18 := mul(355687428096000, 18)

Exp convolution right0 factorial step18 = 6402373705728000

Exp convolution right0 factorial step19 := mul(6402373705728000, 19)

Exp convolution right0 factorial step19 = 121645100408832000

Exp convolution denominator0 := mul(1, 121645100408832000)

Exp convolution denominator0 = 121645100408832000

Exp convolution coefficient term0 := div(-13248496640331026125580781/32064977213018365645815808, 121645100408832000)

Exp convolution coefficient term0 = -41209797661291758429/12132755312575326542353091425992704000

(20/21)^1

Exp convolution x power1 = 20/21

(-21/22)^18

Exp convolution y power18 = 630880792396715529789561/1457498964228107529355264

Exp convolution numerator1 := mul(20/21, 630880792396715529789561/1457498964228107529355264)

Exp convolution numerator1 = 150209712475408459473705/364374741057026882338816

Exp convolution left1 factorial step1 := mul(1, 1)

Exp convolution left1 factorial step1 = 1

Exp convolution right1 factorial step1 := mul(1, 1)

Exp convolution right1 factorial step1 = 1

Exp convolution right1 factorial step2 := mul(1, 2)

Exp convolution right1 factorial step2 = 2

Exp convolution right1 factorial step3 := mul(2, 3)

Exp convolution right1 factorial step3 = 6

Exp convolution right1 factorial step4 := mul(6, 4)

Exp convolution right1 factorial step4 = 24

Exp convolution right1 factorial step5 := mul(24, 5)

Exp convolution right1 factorial step5 = 120

Exp convolution right1 factorial step6 := mul(120, 6)

Exp convolution right1 factorial step6 = 720

Exp convolution right1 factorial step7 := mul(720, 7)

Exp convolution right1 factorial step7 = 5040

Exp convolution right1 factorial step8 := mul(5040, 8)

Exp convolution right1 factorial step8 = 40320

Exp convolution right1 factorial step9 := mul(40320, 9)

Exp convolution right1 factorial step9 = 362880

Exp convolution right1 factorial step10 := mul(362880, 10)

Exp convolution right1 factorial step10 = 3628800

Exp convolution right1 factorial step11 := mul(3628800, 11)

Exp convolution right1 factorial step11 = 39916800

Exp convolution right1 factorial step12 := mul(39916800, 12)

Exp convolution right1 factorial step12 = 479001600

Exp convolution right1 factorial step13 := mul(479001600, 13)

Exp convolution right1 factorial step13 = 6227020800

Exp convolution right1 factorial step14 := mul(6227020800, 14)

Exp convolution right1 factorial step14 = 87178291200

Exp convolution right1 factorial step15 := mul(87178291200, 15)

Exp convolution right1 factorial step15 = 1307674368000

Exp convolution right1 factorial step16 := mul(1307674368000, 16)

Exp convolution right1 factorial step16 = 20922789888000

Exp convolution right1 factorial step17 := mul(20922789888000, 17)

Exp convolution right1 factorial step17 = 355687428096000

Exp convolution right1 factorial step18 := mul(355687428096000, 18)

Exp convolution right1 factorial step18 = 6402373705728000

Exp convolution denominator1 := mul(1, 6402373705728000)

Exp convolution denominator1 = 6402373705728000

Exp convolution coefficient term1 := div(150209712475408459473705/364374741057026882338816, 6402373705728000)

Exp convolution coefficient term1 = 93446253200208069/1451286520642981643822140122726400

(20/21)^2

Exp convolution x power2 = 400/441

(-21/22)^17

Exp convolution y power17 = -30041942495081691894741/66249952919459433152512

Exp convolution numerator2 := mul(400/441, -30041942495081691894741/66249952919459433152512)

Exp convolution numerator2 = -1703057964573792057525/4140622057466214572032

Exp convolution left2 factorial step1 := mul(1, 1)

Exp convolution left2 factorial step1 = 1

Exp convolution left2 factorial step2 := mul(1, 2)

Exp convolution left2 factorial step2 = 2

Exp convolution right2 factorial step1 := mul(1, 1)

Exp convolution right2 factorial step1 = 1

Exp convolution right2 factorial step2 := mul(1, 2)

Exp convolution right2 factorial step2 = 2

Exp convolution right2 factorial step3 := mul(2, 3)

Exp convolution right2 factorial step3 = 6

Exp convolution right2 factorial step4 := mul(6, 4)

Exp convolution right2 factorial step4 = 24

Exp convolution right2 factorial step5 := mul(24, 5)

Exp convolution right2 factorial step5 = 120

Exp convolution right2 factorial step6 := mul(120, 6)

Exp convolution right2 factorial step6 = 720

Exp convolution right2 factorial step7 := mul(720, 7)

Exp convolution right2 factorial step7 = 5040

Exp convolution right2 factorial step8 := mul(5040, 8)

Exp convolution right2 factorial step8 = 40320

Exp convolution right2 factorial step9 := mul(40320, 9)

Exp convolution right2 factorial step9 = 362880

Exp convolution right2 factorial step10 := mul(362880, 10)

Exp convolution right2 factorial step10 = 3628800

Exp convolution right2 factorial step11 := mul(3628800, 11)

Exp convolution right2 factorial step11 = 39916800

Exp convolution right2 factorial step12 := mul(39916800, 12)

Exp convolution right2 factorial step12 = 479001600

Exp convolution right2 factorial step13 := mul(479001600, 13)

Exp convolution right2 factorial step13 = 6227020800

Exp convolution right2 factorial step14 := mul(6227020800, 14)

Exp convolution right2 factorial step14 = 87178291200

Exp convolution right2 factorial step15 := mul(87178291200, 15)

Exp convolution right2 factorial step15 = 1307674368000

Exp convolution right2 factorial step16 := mul(1307674368000, 16)

Exp convolution right2 factorial step16 = 20922789888000

Exp convolution right2 factorial step17 := mul(20922789888000, 17)

Exp convolution right2 factorial step17 = 355687428096000

Exp convolution denominator2 := mul(2, 355687428096000)

Exp convolution denominator2 = 711374856192000

Exp convolution coefficient term2 := div(-1703057964573792057525/4140622057466214572032, 711374856192000)

Exp convolution coefficient term2 = -1907066391840981/3298378456006776463232136642560

(20/21)^3

Exp convolution x power3 = 8000/9261

(-21/22)^16

Exp convolution y power16 = 1430568690241985328321/3011361496339065143296

Exp convolution numerator3 := mul(8000/9261, 1430568690241985328321/3011361496339065143296)

Exp convolution numerator3 = 19309047217389932625/47052523380297892864

Exp convolution left3 factorial step1 := mul(1, 1)

Exp convolution left3 factorial step1 = 1

Exp convolution left3 factorial step2 := mul(1, 2)

Exp convolution left3 factorial step2 = 2

Exp convolution left3 factorial step3 := mul(2, 3)

Exp convolution left3 factorial step3 = 6

Exp convolution right3 factorial step1 := mul(1, 1)

Exp convolution right3 factorial step1 = 1

Exp convolution right3 factorial step2 := mul(1, 2)

Exp convolution right3 factorial step2 = 2

Exp convolution right3 factorial step3 := mul(2, 3)

Exp convolution right3 factorial step3 = 6

Exp convolution right3 factorial step4 := mul(6, 4)

Exp convolution right3 factorial step4 = 24

Exp convolution right3 factorial step5 := mul(24, 5)

Exp convolution right3 factorial step5 = 120

Exp convolution right3 factorial step6 := mul(120, 6)

Exp convolution right3 factorial step6 = 720

Exp convolution right3 factorial step7 := mul(720, 7)

Exp convolution right3 factorial step7 = 5040

Exp convolution right3 factorial step8 := mul(5040, 8)

Exp convolution right3 factorial step8 = 40320

Exp convolution right3 factorial step9 := mul(40320, 9)

Exp convolution right3 factorial step9 = 362880

Exp convolution right3 factorial step10 := mul(362880, 10)

Exp convolution right3 factorial step10 = 3628800

Exp convolution right3 factorial step11 := mul(3628800, 11)

Exp convolution right3 factorial step11 = 39916800

Exp convolution right3 factorial step12 := mul(39916800, 12)

Exp convolution right3 factorial step12 = 479001600

Exp convolution right3 factorial step13 := mul(479001600, 13)

Exp convolution right3 factorial step13 = 6227020800

Exp convolution right3 factorial step14 := mul(6227020800, 14)

Exp convolution right3 factorial step14 = 87178291200

Exp convolution right3 factorial step15 := mul(87178291200, 15)

Exp convolution right3 factorial step15 = 1307674368000

Exp convolution right3 factorial step16 := mul(1307674368000, 16)

Exp convolution right3 factorial step16 = 20922789888000

Exp convolution denominator3 := mul(6, 20922789888000)

Exp convolution denominator3 = 125536739328000

Exp convolution coefficient term3 := div(19309047217389932625/47052523380297892864, 125536739328000)

Exp convolution coefficient term3 = 1441471195647/440959686631921987063119872

(20/21)^4

Exp convolution x power4 = 160000/194481

(-21/22)^15

Exp convolution y power15 = -68122318582951682301/136880068015412051968

Exp convolution numerator4 := mul(160000/194481, -68122318582951682301/136880068015412051968)

Exp convolution numerator4 = -218923437838888125/534687765685203328

Exp convolution left4 factorial step1 := mul(1, 1)

Exp convolution left4 factorial step1 = 1

Exp convolution left4 factorial step2 := mul(1, 2)

Exp convolution left4 factorial step2 = 2

Exp convolution left4 factorial step3 := mul(2, 3)

Exp convolution left4 factorial step3 = 6

Exp convolution left4 factorial step4 := mul(6, 4)

Exp convolution left4 factorial step4 = 24

Exp convolution right4 factorial step1 := mul(1, 1)

Exp convolution right4 factorial step1 = 1

Exp convolution right4 factorial step2 := mul(1, 2)

Exp convolution right4 factorial step2 = 2

Exp convolution right4 factorial step3 := mul(2, 3)

Exp convolution right4 factorial step3 = 6

Exp convolution right4 factorial step4 := mul(6, 4)

Exp convolution right4 factorial step4 = 24

Exp convolution right4 factorial step5 := mul(24, 5)

Exp convolution right4 factorial step5 = 120

Exp convolution right4 factorial step6 := mul(120, 6)

Exp convolution right4 factorial step6 = 720

Exp convolution right4 factorial step7 := mul(720, 7)

Exp convolution right4 factorial step7 = 5040

Exp convolution right4 factorial step8 := mul(5040, 8)

Exp convolution right4 factorial step8 = 40320

Exp convolution right4 factorial step9 := mul(40320, 9)

Exp convolution right4 factorial step9 = 362880

Exp convolution right4 factorial step10 := mul(362880, 10)

Exp convolution right4 factorial step10 = 3628800

Exp convolution right4 factorial step11 := mul(3628800, 11)

Exp convolution right4 factorial step11 = 39916800

Exp convolution right4 factorial step12 := mul(39916800, 12)

Exp convolution right4 factorial step12 = 479001600

Exp convolution right4 factorial step13 := mul(479001600, 13)

Exp convolution right4 factorial step13 = 6227020800

Exp convolution right4 factorial step14 := mul(6227020800, 14)

Exp convolution right4 factorial step14 = 87178291200

Exp convolution right4 factorial step15 := mul(87178291200, 15)

Exp convolution right4 factorial step15 = 1307674368000

Exp convolution denominator4 := mul(24, 1307674368000)

Exp convolution denominator4 = 31384184832000

Exp convolution coefficient term4 := div(-218923437838888125/534687765685203328, 31384184832000)

Exp convolution coefficient term4 = -16343210835/1252726382477051099611136

(20/21)^5

Exp convolution x power5 = 3200000/4084101

(-21/22)^14

Exp convolution y power14 = 3243919932521508681/6221821273427820544

Exp convolution numerator5 := mul(3200000/4084101, 3243919932521508681/6221821273427820544)

Exp convolution numerator5 = 2482125145565625/6075997337331856

Exp convolution left5 factorial step1 := mul(1, 1)

Exp convolution left5 factorial step1 = 1

Exp convolution left5 factorial step2 := mul(1, 2)

Exp convolution left5 factorial step2 = 2

Exp convolution left5 factorial step3 := mul(2, 3)

Exp convolution left5 factorial step3 = 6

Exp convolution left5 factorial step4 := mul(6, 4)

Exp convolution left5 factorial step4 = 24

Exp convolution left5 factorial step5 := mul(24, 5)

Exp convolution left5 factorial step5 = 120

Exp convolution right5 factorial step1 := mul(1, 1)

Exp convolution right5 factorial step1 = 1

Exp convolution right5 factorial step2 := mul(1, 2)

Exp convolution right5 factorial step2 = 2

Exp convolution right5 factorial step3 := mul(2, 3)

Exp convolution right5 factorial step3 = 6

Exp convolution right5 factorial step4 := mul(6, 4)

Exp convolution right5 factorial step4 = 24

Exp convolution right5 factorial step5 := mul(24, 5)

Exp convolution right5 factorial step5 = 120

Exp convolution right5 factorial step6 := mul(120, 6)

Exp convolution right5 factorial step6 = 720

Exp convolution right5 factorial step7 := mul(720, 7)

Exp convolution right5 factorial step7 = 5040

Exp convolution right5 factorial step8 := mul(5040, 8)

Exp convolution right5 factorial step8 = 40320

Exp convolution right5 factorial step9 := mul(40320, 9)

Exp convolution right5 factorial step9 = 362880

Exp convolution right5 factorial step10 := mul(362880, 10)

Exp convolution right5 factorial step10 = 3628800

Exp convolution right5 factorial step11 := mul(3628800, 11)

Exp convolution right5 factorial step11 = 39916800

Exp convolution right5 factorial step12 := mul(39916800, 12)

Exp convolution right5 factorial step12 = 479001600

Exp convolution right5 factorial step13 := mul(479001600, 13)

Exp convolution right5 factorial step13 = 6227020800

Exp convolution right5 factorial step14 := mul(6227020800, 14)

Exp convolution right5 factorial step14 = 87178291200

Exp convolution denominator5 := mul(120, 87178291200)

Exp convolution denominator5 = 10461394944000

Exp convolution coefficient term5 := div(2482125145565625/6075997337331856, 10461394944000)

Exp convolution coefficient term5 = 555891525/14235527073602853404672

(20/21)^6

Exp convolution x power6 = 64000000/85766121

(-21/22)^13

Exp convolution y power13 = -154472377739119461/282810057883082752

Exp convolution numerator6 := mul(64000000/85766121, -154472377739119461/282810057883082752)

Exp convolution numerator6 = -28142008453125/69045424287862

Exp convolution left6 factorial step1 := mul(1, 1)

Exp convolution left6 factorial step1 = 1

Exp convolution left6 factorial step2 := mul(1, 2)

Exp convolution left6 factorial step2 = 2

Exp convolution left6 factorial step3 := mul(2, 3)

Exp convolution left6 factorial step3 = 6

Exp convolution left6 factorial step4 := mul(6, 4)

Exp convolution left6 factorial step4 = 24

Exp convolution left6 factorial step5 := mul(24, 5)

Exp convolution left6 factorial step5 = 120

Exp convolution left6 factorial step6 := mul(120, 6)

Exp convolution left6 factorial step6 = 720

Exp convolution right6 factorial step1 := mul(1, 1)

Exp convolution right6 factorial step1 = 1

Exp convolution right6 factorial step2 := mul(1, 2)

Exp convolution right6 factorial step2 = 2

Exp convolution right6 factorial step3 := mul(2, 3)

Exp convolution right6 factorial step3 = 6

Exp convolution right6 factorial step4 := mul(6, 4)

Exp convolution right6 factorial step4 = 24

Exp convolution right6 factorial step5 := mul(24, 5)

Exp convolution right6 factorial step5 = 120

Exp convolution right6 factorial step6 := mul(120, 6)

Exp convolution right6 factorial step6 = 720

Exp convolution right6 factorial step7 := mul(720, 7)

Exp convolution right6 factorial step7 = 5040

Exp convolution right6 factorial step8 := mul(5040, 8)

Exp convolution right6 factorial step8 = 40320

Exp convolution right6 factorial step9 := mul(40320, 9)

Exp convolution right6 factorial step9 = 362880

Exp convolution right6 factorial step10 := mul(362880, 10)

Exp convolution right6 factorial step10 = 3628800

Exp convolution right6 factorial step11 := mul(3628800, 11)

Exp convolution right6 factorial step11 = 39916800

Exp convolution right6 factorial step12 := mul(39916800, 12)

Exp convolution right6 factorial step12 = 479001600

Exp convolution right6 factorial step13 := mul(479001600, 13)

Exp convolution right6 factorial step13 = 6227020800

Exp convolution denominator6 := mul(720, 6227020800)

Exp convolution denominator6 = 4483454976000

Exp convolution coefficient term6 := div(-28142008453125/69045424287862, 4483454976000)

Exp convolution coefficient term6 = -14706125/161767353109123334144

(20/21)^7

Exp convolution x power7 = 1280000000/1801088541

(-21/22)^12

Exp convolution y power12 = 7355827511386641/12855002631049216

Exp convolution numerator7 := mul(1280000000/1801088541, 7355827511386641/12855002631049216)

Exp convolution numerator7 = 1276281562500/3138428376721

Exp convolution left7 factorial step1 := mul(1, 1)

Exp convolution left7 factorial step1 = 1

Exp convolution left7 factorial step2 := mul(1, 2)

Exp convolution left7 factorial step2 = 2

Exp convolution left7 factorial step3 := mul(2, 3)

Exp convolution left7 factorial step3 = 6

Exp convolution left7 factorial step4 := mul(6, 4)

Exp convolution left7 factorial step4 = 24

Exp convolution left7 factorial step5 := mul(24, 5)

Exp convolution left7 factorial step5 = 120

Exp convolution left7 factorial step6 := mul(120, 6)

Exp convolution left7 factorial step6 = 720

Exp convolution left7 factorial step7 := mul(720, 7)

Exp convolution left7 factorial step7 = 5040

Exp convolution right7 factorial step1 := mul(1, 1)

Exp convolution right7 factorial step1 = 1

Exp convolution right7 factorial step2 := mul(1, 2)

Exp convolution right7 factorial step2 = 2

Exp convolution right7 factorial step3 := mul(2, 3)

Exp convolution right7 factorial step3 = 6

Exp convolution right7 factorial step4 := mul(6, 4)

Exp convolution right7 factorial step4 = 24

Exp convolution right7 factorial step5 := mul(24, 5)

Exp convolution right7 factorial step5 = 120

Exp convolution right7 factorial step6 := mul(120, 6)

Exp convolution right7 factorial step6 = 720

Exp convolution right7 factorial step7 := mul(720, 7)

Exp convolution right7 factorial step7 = 5040

Exp convolution right7 factorial step8 := mul(5040, 8)

Exp convolution right7 factorial step8 = 40320

Exp convolution right7 factorial step9 := mul(40320, 9)

Exp convolution right7 factorial step9 = 362880

Exp convolution right7 factorial step10 := mul(362880, 10)

Exp convolution right7 factorial step10 = 3628800

Exp convolution right7 factorial step11 := mul(3628800, 11)

Exp convolution right7 factorial step11 = 39916800

Exp convolution right7 factorial step12 := mul(39916800, 12)

Exp convolution right7 factorial step12 = 479001600

Exp convolution denominator7 := mul(5040, 479001600)

Exp convolution denominator7 = 2414168064000

Exp convolution coefficient term7 := div(1276281562500/3138428376721, 2414168064000)

Exp convolution coefficient term7 = 214375/1272645260473872384

(20/21)^8

Exp convolution x power8 = 25600000000/37822859361

(-21/22)^11

Exp convolution y power11 = -350277500542221/584318301411328

Exp convolution numerator8 := mul(25600000000/37822859361, -350277500542221/584318301411328)

Exp convolution numerator8 = -115762500000/285311670611

Exp convolution left8 factorial step1 := mul(1, 1)

Exp convolution left8 factorial step1 = 1

Exp convolution left8 factorial step2 := mul(1, 2)

Exp convolution left8 factorial step2 = 2

Exp convolution left8 factorial step3 := mul(2, 3)

Exp convolution left8 factorial step3 = 6

Exp convolution left8 factorial step4 := mul(6, 4)

Exp convolution left8 factorial step4 = 24

Exp convolution left8 factorial step5 := mul(24, 5)

Exp convolution left8 factorial step5 = 120

Exp convolution left8 factorial step6 := mul(120, 6)

Exp convolution left8 factorial step6 = 720

Exp convolution left8 factorial step7 := mul(720, 7)

Exp convolution left8 factorial step7 = 5040

Exp convolution left8 factorial step8 := mul(5040, 8)

Exp convolution left8 factorial step8 = 40320

Exp convolution right8 factorial step1 := mul(1, 1)

Exp convolution right8 factorial step1 = 1

Exp convolution right8 factorial step2 := mul(1, 2)

Exp convolution right8 factorial step2 = 2

Exp convolution right8 factorial step3 := mul(2, 3)

Exp convolution right8 factorial step3 = 6

Exp convolution right8 factorial step4 := mul(6, 4)

Exp convolution right8 factorial step4 = 24

Exp convolution right8 factorial step5 := mul(24, 5)

Exp convolution right8 factorial step5 = 120

Exp convolution right8 factorial step6 := mul(120, 6)

Exp convolution right8 factorial step6 = 720

Exp convolution right8 factorial step7 := mul(720, 7)

Exp convolution right8 factorial step7 = 5040

Exp convolution right8 factorial step8 := mul(5040, 8)

Exp convolution right8 factorial step8 = 40320

Exp convolution right8 factorial step9 := mul(40320, 9)

Exp convolution right8 factorial step9 = 362880

Exp convolution right8 factorial step10 := mul(362880, 10)

Exp convolution right8 factorial step10 = 3628800

Exp convolution right8 factorial step11 := mul(3628800, 11)

Exp convolution right8 factorial step11 = 39916800

Exp convolution denominator8 := mul(40320, 39916800)

Exp convolution denominator8 = 1609445376000

Exp convolution coefficient term8 := div(-115762500000/285311670611, 1609445376000)

Exp convolution coefficient term8 = -21875/86771267759582208

(20/21)^9

Exp convolution x power9 = 512000000000/794280046581

(-21/22)^10

Exp convolution y power10 = 16679880978201/26559922791424

Exp convolution numerator9 := mul(512000000000/794280046581, 16679880978201/26559922791424)

Exp convolution numerator9 = 10500000000/25937424601

Exp convolution left9 factorial step1 := mul(1, 1)

Exp convolution left9 factorial step1 = 1

Exp convolution left9 factorial step2 := mul(1, 2)

Exp convolution left9 factorial step2 = 2

Exp convolution left9 factorial step3 := mul(2, 3)

Exp convolution left9 factorial step3 = 6

Exp convolution left9 factorial step4 := mul(6, 4)

Exp convolution left9 factorial step4 = 24

Exp convolution left9 factorial step5 := mul(24, 5)

Exp convolution left9 factorial step5 = 120

Exp convolution left9 factorial step6 := mul(120, 6)

Exp convolution left9 factorial step6 = 720

Exp convolution left9 factorial step7 := mul(720, 7)

Exp convolution left9 factorial step7 = 5040

Exp convolution left9 factorial step8 := mul(5040, 8)

Exp convolution left9 factorial step8 = 40320

Exp convolution left9 factorial step9 := mul(40320, 9)

Exp convolution left9 factorial step9 = 362880

Exp convolution right9 factorial step1 := mul(1, 1)

Exp convolution right9 factorial step1 = 1

Exp convolution right9 factorial step2 := mul(1, 2)

Exp convolution right9 factorial step2 = 2

Exp convolution right9 factorial step3 := mul(2, 3)

Exp convolution right9 factorial step3 = 6

Exp convolution right9 factorial step4 := mul(6, 4)

Exp convolution right9 factorial step4 = 24

Exp convolution right9 factorial step5 := mul(24, 5)

Exp convolution right9 factorial step5 = 120

Exp convolution right9 factorial step6 := mul(120, 6)

Exp convolution right9 factorial step6 = 720

Exp convolution right9 factorial step7 := mul(720, 7)

Exp convolution right9 factorial step7 = 5040

Exp convolution right9 factorial step8 := mul(5040, 8)

Exp convolution right9 factorial step8 = 40320

Exp convolution right9 factorial step9 := mul(40320, 9)

Exp convolution right9 factorial step9 = 362880

Exp convolution right9 factorial step10 := mul(362880, 10)

Exp convolution right9 factorial step10 = 3628800

Exp convolution denominator9 := mul(362880, 3628800)

Exp convolution denominator9 = 1316818944000

Exp convolution coefficient term9 := div(10500000000/25937424601, 1316818944000)

Exp convolution coefficient term9 = 15625/50825732251738752

(20/21)^10

Exp convolution x power10 = 10240000000000/16679880978201

(-21/22)^9

Exp convolution y power9 = -794280046581/1207269217792

Exp convolution numerator10 := mul(10240000000000/16679880978201, -794280046581/1207269217792)

Exp convolution numerator10 = -20000000000/49516901511

Exp convolution left10 factorial step1 := mul(1, 1)

Exp convolution left10 factorial step1 = 1

Exp convolution left10 factorial step2 := mul(1, 2)

Exp convolution left10 factorial step2 = 2

Exp convolution left10 factorial step3 := mul(2, 3)

Exp convolution left10 factorial step3 = 6

Exp convolution left10 factorial step4 := mul(6, 4)

Exp convolution left10 factorial step4 = 24

Exp convolution left10 factorial step5 := mul(24, 5)

Exp convolution left10 factorial step5 = 120

Exp convolution left10 factorial step6 := mul(120, 6)

Exp convolution left10 factorial step6 = 720

Exp convolution left10 factorial step7 := mul(720, 7)

Exp convolution left10 factorial step7 = 5040

Exp convolution left10 factorial step8 := mul(5040, 8)

Exp convolution left10 factorial step8 = 40320

Exp convolution left10 factorial step9 := mul(40320, 9)

Exp convolution left10 factorial step9 = 362880

Exp convolution left10 factorial step10 := mul(362880, 10)

Exp convolution left10 factorial step10 = 3628800

Exp convolution right10 factorial step1 := mul(1, 1)

Exp convolution right10 factorial step1 = 1

Exp convolution right10 factorial step2 := mul(1, 2)

Exp convolution right10 factorial step2 = 2

Exp convolution right10 factorial step3 := mul(2, 3)

Exp convolution right10 factorial step3 = 6

Exp convolution right10 factorial step4 := mul(6, 4)

Exp convolution right10 factorial step4 = 24

Exp convolution right10 factorial step5 := mul(24, 5)

Exp convolution right10 factorial step5 = 120

Exp convolution right10 factorial step6 := mul(120, 6)

Exp convolution right10 factorial step6 = 720

Exp convolution right10 factorial step7 := mul(720, 7)

Exp convolution right10 factorial step7 = 5040

Exp convolution right10 factorial step8 := mul(5040, 8)

Exp convolution right10 factorial step8 = 40320

Exp convolution right10 factorial step9 := mul(40320, 9)

Exp convolution right10 factorial step9 = 362880

Exp convolution denominator10 := mul(3628800, 362880)

Exp convolution denominator10 = 1316818944000

Exp convolution coefficient term10 := div(-20000000000/49516901511, 1316818944000)

Exp convolution coefficient term10 = -78125/254706226397918064

(20/21)^11

Exp convolution x power11 = 204800000000000/350277500542221

(-21/22)^8

Exp convolution y power8 = 37822859361/54875873536

Exp convolution numerator11 := mul(204800000000000/350277500542221, 37822859361/54875873536)

Exp convolution numerator11 = 800000000000/1985177596941

Exp convolution left11 factorial step1 := mul(1, 1)

Exp convolution left11 factorial step1 = 1

Exp convolution left11 factorial step2 := mul(1, 2)

Exp convolution left11 factorial step2 = 2

Exp convolution left11 factorial step3 := mul(2, 3)

Exp convolution left11 factorial step3 = 6

Exp convolution left11 factorial step4 := mul(6, 4)

Exp convolution left11 factorial step4 = 24

Exp convolution left11 factorial step5 := mul(24, 5)

Exp convolution left11 factorial step5 = 120

Exp convolution left11 factorial step6 := mul(120, 6)

Exp convolution left11 factorial step6 = 720

Exp convolution left11 factorial step7 := mul(720, 7)

Exp convolution left11 factorial step7 = 5040

Exp convolution left11 factorial step8 := mul(5040, 8)

Exp convolution left11 factorial step8 = 40320

Exp convolution left11 factorial step9 := mul(40320, 9)

Exp convolution left11 factorial step9 = 362880

Exp convolution left11 factorial step10 := mul(362880, 10)

Exp convolution left11 factorial step10 = 3628800

Exp convolution left11 factorial step11 := mul(3628800, 11)

Exp convolution left11 factorial step11 = 39916800

Exp convolution right11 factorial step1 := mul(1, 1)

Exp convolution right11 factorial step1 = 1

Exp convolution right11 factorial step2 := mul(1, 2)

Exp convolution right11 factorial step2 = 2

Exp convolution right11 factorial step3 := mul(2, 3)

Exp convolution right11 factorial step3 = 6

Exp convolution right11 factorial step4 := mul(6, 4)

Exp convolution right11 factorial step4 = 24

Exp convolution right11 factorial step5 := mul(24, 5)

Exp convolution right11 factorial step5 = 120

Exp convolution right11 factorial step6 := mul(120, 6)

Exp convolution right11 factorial step6 = 720

Exp convolution right11 factorial step7 := mul(720, 7)

Exp convolution right11 factorial step7 = 5040

Exp convolution right11 factorial step8 := mul(5040, 8)

Exp convolution right11 factorial step8 = 40320

Exp convolution denominator11 := mul(39916800, 40320)

Exp convolution denominator11 = 1609445376000

Exp convolution coefficient term11 := div(800000000000/1985177596941, 1609445376000)

Exp convolution coefficient term11 = 390625/1560075636687248142

(20/21)^12

Exp convolution x power12 = 4096000000000000/7355827511386641

(-21/22)^7

Exp convolution y power7 = -1801088541/2494357888

Exp convolution numerator12 := mul(4096000000000000/7355827511386641, -1801088541/2494357888)

Exp convolution numerator12 = -32000000000000/79587574568271

Exp convolution left12 factorial step1 := mul(1, 1)

Exp convolution left12 factorial step1 = 1

Exp convolution left12 factorial step2 := mul(1, 2)

Exp convolution left12 factorial step2 = 2

Exp convolution left12 factorial step3 := mul(2, 3)

Exp convolution left12 factorial step3 = 6

Exp convolution left12 factorial step4 := mul(6, 4)

Exp convolution left12 factorial step4 = 24

Exp convolution left12 factorial step5 := mul(24, 5)

Exp convolution left12 factorial step5 = 120

Exp convolution left12 factorial step6 := mul(120, 6)

Exp convolution left12 factorial step6 = 720

Exp convolution left12 factorial step7 := mul(720, 7)

Exp convolution left12 factorial step7 = 5040

Exp convolution left12 factorial step8 := mul(5040, 8)

Exp convolution left12 factorial step8 = 40320

Exp convolution left12 factorial step9 := mul(40320, 9)

Exp convolution left12 factorial step9 = 362880

Exp convolution left12 factorial step10 := mul(362880, 10)

Exp convolution left12 factorial step10 = 3628800

Exp convolution left12 factorial step11 := mul(3628800, 11)

Exp convolution left12 factorial step11 = 39916800

Exp convolution left12 factorial step12 := mul(39916800, 12)

Exp convolution left12 factorial step12 = 479001600

Exp convolution right12 factorial step1 := mul(1, 1)

Exp convolution right12 factorial step1 = 1

Exp convolution right12 factorial step2 := mul(1, 2)

Exp convolution right12 factorial step2 = 2

Exp convolution right12 factorial step3 := mul(2, 3)

Exp convolution right12 factorial step3 = 6

Exp convolution right12 factorial step4 := mul(6, 4)

Exp convolution right12 factorial step4 = 24

Exp convolution right12 factorial step5 := mul(24, 5)

Exp convolution right12 factorial step5 = 120

Exp convolution right12 factorial step6 := mul(120, 6)

Exp convolution right12 factorial step6 = 720

Exp convolution right12 factorial step7 := mul(720, 7)

Exp convolution right12 factorial step7 = 5040

Exp convolution denominator12 := mul(479001600, 5040)

Exp convolution denominator12 = 2414168064000

Exp convolution coefficient term12 := div(-32000000000000/79587574568271, 2414168064000)

Exp convolution coefficient term12 = -15625000/93817275788055876903

(20/21)^13

Exp convolution x power13 = 81920000000000000/154472377739119461

(-21/22)^6

Exp convolution y power6 = 85766121/113379904

Exp convolution numerator13 := mul(81920000000000000/154472377739119461, 85766121/113379904)

Exp convolution numerator13 = 1280000000000000/3190738216782501

Exp convolution left13 factorial step1 := mul(1, 1)

Exp convolution left13 factorial step1 = 1

Exp convolution left13 factorial step2 := mul(1, 2)

Exp convolution left13 factorial step2 = 2

Exp convolution left13 factorial step3 := mul(2, 3)

Exp convolution left13 factorial step3 = 6

Exp convolution left13 factorial step4 := mul(6, 4)

Exp convolution left13 factorial step4 = 24

Exp convolution left13 factorial step5 := mul(24, 5)

Exp convolution left13 factorial step5 = 120

Exp convolution left13 factorial step6 := mul(120, 6)

Exp convolution left13 factorial step6 = 720

Exp convolution left13 factorial step7 := mul(720, 7)

Exp convolution left13 factorial step7 = 5040

Exp convolution left13 factorial step8 := mul(5040, 8)

Exp convolution left13 factorial step8 = 40320

Exp convolution left13 factorial step9 := mul(40320, 9)

Exp convolution left13 factorial step9 = 362880

Exp convolution left13 factorial step10 := mul(362880, 10)

Exp convolution left13 factorial step10 = 3628800

Exp convolution left13 factorial step11 := mul(3628800, 11)

Exp convolution left13 factorial step11 = 39916800

Exp convolution left13 factorial step12 := mul(39916800, 12)

Exp convolution left13 factorial step12 = 479001600

Exp convolution left13 factorial step13 := mul(479001600, 13)

Exp convolution left13 factorial step13 = 6227020800

Exp convolution right13 factorial step1 := mul(1, 1)

Exp convolution right13 factorial step1 = 1

Exp convolution right13 factorial step2 := mul(1, 2)

Exp convolution right13 factorial step2 = 2

Exp convolution right13 factorial step3 := mul(2, 3)

Exp convolution right13 factorial step3 = 6

Exp convolution right13 factorial step4 := mul(6, 4)

Exp convolution right13 factorial step4 = 24

Exp convolution right13 factorial step5 := mul(24, 5)

Exp convolution right13 factorial step5 = 120

Exp convolution right13 factorial step6 := mul(120, 6)

Exp convolution right13 factorial step6 = 720

Exp convolution denominator13 := mul(6227020800, 720)

Exp convolution denominator13 = 4483454976000

Exp convolution coefficient term13 := div(1280000000000000/3190738216782501, 4483454976000)

Exp convolution coefficient term13 = 625000000/6985122624583433016687

(20/21)^14

Exp convolution x power14 = 1638400000000000000/3243919932521508681

(-21/22)^5

Exp convolution y power5 = -4084101/5153632

Exp convolution numerator14 := mul(1638400000000000000/3243919932521508681, -4084101/5153632)

Exp convolution numerator14 = -51200000000000000/127919595781916631

Exp convolution left14 factorial step1 := mul(1, 1)

Exp convolution left14 factorial step1 = 1

Exp convolution left14 factorial step2 := mul(1, 2)

Exp convolution left14 factorial step2 = 2

Exp convolution left14 factorial step3 := mul(2, 3)

Exp convolution left14 factorial step3 = 6

Exp convolution left14 factorial step4 := mul(6, 4)

Exp convolution left14 factorial step4 = 24

Exp convolution left14 factorial step5 := mul(24, 5)

Exp convolution left14 factorial step5 = 120

Exp convolution left14 factorial step6 := mul(120, 6)

Exp convolution left14 factorial step6 = 720

Exp convolution left14 factorial step7 := mul(720, 7)

Exp convolution left14 factorial step7 = 5040

Exp convolution left14 factorial step8 := mul(5040, 8)

Exp convolution left14 factorial step8 = 40320

Exp convolution left14 factorial step9 := mul(40320, 9)

Exp convolution left14 factorial step9 = 362880

Exp convolution left14 factorial step10 := mul(362880, 10)

Exp convolution left14 factorial step10 = 3628800

Exp convolution left14 factorial step11 := mul(3628800, 11)

Exp convolution left14 factorial step11 = 39916800

Exp convolution left14 factorial step12 := mul(39916800, 12)

Exp convolution left14 factorial step12 = 479001600

Exp convolution left14 factorial step13 := mul(479001600, 13)

Exp convolution left14 factorial step13 = 6227020800

Exp convolution left14 factorial step14 := mul(6227020800, 14)

Exp convolution left14 factorial step14 = 87178291200

Exp convolution right14 factorial step1 := mul(1, 1)

Exp convolution right14 factorial step1 = 1

Exp convolution right14 factorial step2 := mul(1, 2)

Exp convolution right14 factorial step2 = 2

Exp convolution right14 factorial step3 := mul(2, 3)

Exp convolution right14 factorial step3 = 6

Exp convolution right14 factorial step4 := mul(6, 4)

Exp convolution right14 factorial step4 = 24

Exp convolution right14 factorial step5 := mul(24, 5)

Exp convolution right14 factorial step5 = 120

Exp convolution denominator14 := mul(87178291200, 120)

Exp convolution denominator14 = 10461394944000

Exp convolution coefficient term14 := div(-51200000000000000/127919595781916631, 10461394944000)

Exp convolution coefficient term14 = -25000000000/653426470972395688560993

(20/21)^15

Exp convolution x power15 = 32768000000000000000/68122318582951682301

(-21/22)^4

Exp convolution y power4 = 194481/234256

Exp convolution numerator15 := mul(32768000000000000000/68122318582951682301, 194481/234256)

Exp convolution numerator15 = 2048000000000000000/5128412885438657661

Exp convolution left15 factorial step1 := mul(1, 1)

Exp convolution left15 factorial step1 = 1

Exp convolution left15 factorial step2 := mul(1, 2)

Exp convolution left15 factorial step2 = 2

Exp convolution left15 factorial step3 := mul(2, 3)

Exp convolution left15 factorial step3 = 6

Exp convolution left15 factorial step4 := mul(6, 4)

Exp convolution left15 factorial step4 = 24

Exp convolution left15 factorial step5 := mul(24, 5)

Exp convolution left15 factorial step5 = 120

Exp convolution left15 factorial step6 := mul(120, 6)

Exp convolution left15 factorial step6 = 720

Exp convolution left15 factorial step7 := mul(720, 7)

Exp convolution left15 factorial step7 = 5040

Exp convolution left15 factorial step8 := mul(5040, 8)

Exp convolution left15 factorial step8 = 40320

Exp convolution left15 factorial step9 := mul(40320, 9)

Exp convolution left15 factorial step9 = 362880

Exp convolution left15 factorial step10 := mul(362880, 10)

Exp convolution left15 factorial step10 = 3628800

Exp convolution left15 factorial step11 := mul(3628800, 11)

Exp convolution left15 factorial step11 = 39916800

Exp convolution left15 factorial step12 := mul(39916800, 12)

Exp convolution left15 factorial step12 = 479001600

Exp convolution left15 factorial step13 := mul(479001600, 13)

Exp convolution left15 factorial step13 = 6227020800

Exp convolution left15 factorial step14 := mul(6227020800, 14)

Exp convolution left15 factorial step14 = 87178291200

Exp convolution left15 factorial step15 := mul(87178291200, 15)

Exp convolution left15 factorial step15 = 1307674368000

Exp convolution right15 factorial step1 := mul(1, 1)

Exp convolution right15 factorial step1 = 1

Exp convolution right15 factorial step2 := mul(1, 2)

Exp convolution right15 factorial step2 = 2

Exp convolution right15 factorial step3 := mul(2, 3)

Exp convolution right15 factorial step3 = 6

Exp convolution right15 factorial step4 := mul(6, 4)

Exp convolution right15 factorial step4 = 24

Exp convolution denominator15 := mul(1307674368000, 24)

Exp convolution denominator15 = 31384184832000

Exp convolution coefficient term15 := div(2048000000000000000/5128412885438657661, 31384184832000)

Exp convolution coefficient term15 = 1000000000000/78589383736043590542381249

(20/21)^16

Exp convolution x power16 = 655360000000000000000/1430568690241985328321

(-21/22)^3

Exp convolution y power3 = -9261/10648

Exp convolution numerator16 := mul(655360000000000000000/1430568690241985328321, -9261/10648)

Exp convolution numerator16 = -81920000000000000000/205602734770768002591

Exp convolution left16 factorial step1 := mul(1, 1)

Exp convolution left16 factorial step1 = 1

Exp convolution left16 factorial step2 := mul(1, 2)

Exp convolution left16 factorial step2 = 2

Exp convolution left16 factorial step3 := mul(2, 3)

Exp convolution left16 factorial step3 = 6

Exp convolution left16 factorial step4 := mul(6, 4)

Exp convolution left16 factorial step4 = 24

Exp convolution left16 factorial step5 := mul(24, 5)

Exp convolution left16 factorial step5 = 120

Exp convolution left16 factorial step6 := mul(120, 6)

Exp convolution left16 factorial step6 = 720

Exp convolution left16 factorial step7 := mul(720, 7)

Exp convolution left16 factorial step7 = 5040

Exp convolution left16 factorial step8 := mul(5040, 8)

Exp convolution left16 factorial step8 = 40320

Exp convolution left16 factorial step9 := mul(40320, 9)

Exp convolution left16 factorial step9 = 362880

Exp convolution left16 factorial step10 := mul(362880, 10)

Exp convolution left16 factorial step10 = 3628800

Exp convolution left16 factorial step11 := mul(3628800, 11)

Exp convolution left16 factorial step11 = 39916800

Exp convolution left16 factorial step12 := mul(39916800, 12)

Exp convolution left16 factorial step12 = 479001600

Exp convolution left16 factorial step13 := mul(479001600, 13)

Exp convolution left16 factorial step13 = 6227020800

Exp convolution left16 factorial step14 := mul(6227020800, 14)

Exp convolution left16 factorial step14 = 87178291200

Exp convolution left16 factorial step15 := mul(87178291200, 15)

Exp convolution left16 factorial step15 = 1307674368000

Exp convolution left16 factorial step16 := mul(1307674368000, 16)

Exp convolution left16 factorial step16 = 20922789888000

Exp convolution right16 factorial step1 := mul(1, 1)

Exp convolution right16 factorial step1 = 1

Exp convolution right16 factorial step2 := mul(1, 2)

Exp convolution right16 factorial step2 = 2

Exp convolution right16 factorial step3 := mul(2, 3)

Exp convolution right16 factorial step3 = 6

Exp convolution denominator16 := mul(20922789888000, 6)

Exp convolution denominator16 = 125536739328000

Exp convolution coefficient term16 := div(-81920000000000000000/205602734770768002591, 125536739328000)

Exp convolution coefficient term16 = -10000000000000/3150719838872293039017284619

(20/21)^17

Exp convolution x power17 = 13107200000000000000000/30041942495081691894741

(-21/22)^2

Exp convolution y power2 = 441/484

Exp convolution numerator17 := mul(13107200000000000000000/30041942495081691894741, 441/484)

Exp convolution numerator17 = 3276800000000000000000/8242800548537153558421

Exp convolution left17 factorial step1 := mul(1, 1)

Exp convolution left17 factorial step1 = 1

Exp convolution left17 factorial step2 := mul(1, 2)

Exp convolution left17 factorial step2 = 2

Exp convolution left17 factorial step3 := mul(2, 3)

Exp convolution left17 factorial step3 = 6

Exp convolution left17 factorial step4 := mul(6, 4)

Exp convolution left17 factorial step4 = 24

Exp convolution left17 factorial step5 := mul(24, 5)

Exp convolution left17 factorial step5 = 120

Exp convolution left17 factorial step6 := mul(120, 6)

Exp convolution left17 factorial step6 = 720

Exp convolution left17 factorial step7 := mul(720, 7)

Exp convolution left17 factorial step7 = 5040

Exp convolution left17 factorial step8 := mul(5040, 8)

Exp convolution left17 factorial step8 = 40320

Exp convolution left17 factorial step9 := mul(40320, 9)

Exp convolution left17 factorial step9 = 362880

Exp convolution left17 factorial step10 := mul(362880, 10)

Exp convolution left17 factorial step10 = 3628800

Exp convolution left17 factorial step11 := mul(3628800, 11)

Exp convolution left17 factorial step11 = 39916800

Exp convolution left17 factorial step12 := mul(39916800, 12)

Exp convolution left17 factorial step12 = 479001600

Exp convolution left17 factorial step13 := mul(479001600, 13)

Exp convolution left17 factorial step13 = 6227020800

Exp convolution left17 factorial step14 := mul(6227020800, 14)

Exp convolution left17 factorial step14 = 87178291200

Exp convolution left17 factorial step15 := mul(87178291200, 15)

Exp convolution left17 factorial step15 = 1307674368000

Exp convolution left17 factorial step16 := mul(1307674368000, 16)

Exp convolution left17 factorial step16 = 20922789888000

Exp convolution left17 factorial step17 := mul(20922789888000, 17)

Exp convolution left17 factorial step17 = 355687428096000

Exp convolution right17 factorial step1 := mul(1, 1)

Exp convolution right17 factorial step1 = 1

Exp convolution right17 factorial step2 := mul(1, 2)

Exp convolution right17 factorial step2 = 2

Exp convolution denominator17 := mul(355687428096000, 2)

Exp convolution denominator17 = 711374856192000

Exp convolution coefficient term17 := div(3276800000000000000000/8242800548537153558421, 711374856192000)

Exp convolution coefficient term17 = 400000000000000/715786261576532754954926751171

(20/21)^18

Exp convolution x power18 = 262144000000000000000000/630880792396715529789561

(-21/22)^1

Exp convolution y power1 = -21/22

Exp convolution numerator18 := mul(262144000000000000000000/630880792396715529789561, -21/22)

Exp convolution numerator18 = -131072000000000000000000/330461367445898610842151

Exp convolution left18 factorial step1 := mul(1, 1)

Exp convolution left18 factorial step1 = 1

Exp convolution left18 factorial step2 := mul(1, 2)

Exp convolution left18 factorial step2 = 2

Exp convolution left18 factorial step3 := mul(2, 3)

Exp convolution left18 factorial step3 = 6

Exp convolution left18 factorial step4 := mul(6, 4)

Exp convolution left18 factorial step4 = 24

Exp convolution left18 factorial step5 := mul(24, 5)

Exp convolution left18 factorial step5 = 120

Exp convolution left18 factorial step6 := mul(120, 6)

Exp convolution left18 factorial step6 = 720

Exp convolution left18 factorial step7 := mul(720, 7)

Exp convolution left18 factorial step7 = 5040

Exp convolution left18 factorial step8 := mul(5040, 8)

Exp convolution left18 factorial step8 = 40320

Exp convolution left18 factorial step9 := mul(40320, 9)

Exp convolution left18 factorial step9 = 362880

Exp convolution left18 factorial step10 := mul(362880, 10)

Exp convolution left18 factorial step10 = 3628800

Exp convolution left18 factorial step11 := mul(3628800, 11)

Exp convolution left18 factorial step11 = 39916800

Exp convolution left18 factorial step12 := mul(39916800, 12)

Exp convolution left18 factorial step12 = 479001600

Exp convolution left18 factorial step13 := mul(479001600, 13)

Exp convolution left18 factorial step13 = 6227020800

Exp convolution left18 factorial step14 := mul(6227020800, 14)

Exp convolution left18 factorial step14 = 87178291200

Exp convolution left18 factorial step15 := mul(87178291200, 15)

Exp convolution left18 factorial step15 = 1307674368000

Exp convolution left18 factorial step16 := mul(1307674368000, 16)

Exp convolution left18 factorial step16 = 20922789888000

Exp convolution left18 factorial step17 := mul(20922789888000, 17)

Exp convolution left18 factorial step17 = 355687428096000

Exp convolution left18 factorial step18 := mul(355687428096000, 18)

Exp convolution left18 factorial step18 = 6402373705728000

Exp convolution right18 factorial step1 := mul(1, 1)

Exp convolution right18 factorial step1 = 1

Exp convolution denominator18 := mul(6402373705728000, 1)

Exp convolution denominator18 = 6402373705728000

Exp convolution coefficient term18 := div(-131072000000000000000000/330461367445898610842151, 6402373705728000)

Exp convolution coefficient term18 = -16000000000000000/258268697472478045856009479581609

(20/21)^19

Exp convolution x power19 = 5242880000000000000000000/13248496640331026125580781

(-21/22)^0

Exp convolution y power0 = 1

Exp convolution numerator19 := mul(5242880000000000000000000/13248496640331026125580781, 1)

Exp convolution numerator19 = 5242880000000000000000000/13248496640331026125580781

Exp convolution left19 factorial step1 := mul(1, 1)

Exp convolution left19 factorial step1 = 1

Exp convolution left19 factorial step2 := mul(1, 2)

Exp convolution left19 factorial step2 = 2

Exp convolution left19 factorial step3 := mul(2, 3)

Exp convolution left19 factorial step3 = 6

Exp convolution left19 factorial step4 := mul(6, 4)

Exp convolution left19 factorial step4 = 24

Exp convolution left19 factorial step5 := mul(24, 5)

Exp convolution left19 factorial step5 = 120

Exp convolution left19 factorial step6 := mul(120, 6)

Exp convolution left19 factorial step6 = 720

Exp convolution left19 factorial step7 := mul(720, 7)

Exp convolution left19 factorial step7 = 5040

Exp convolution left19 factorial step8 := mul(5040, 8)

Exp convolution left19 factorial step8 = 40320

Exp convolution left19 factorial step9 := mul(40320, 9)

Exp convolution left19 factorial step9 = 362880

Exp convolution left19 factorial step10 := mul(362880, 10)

Exp convolution left19 factorial step10 = 3628800

Exp convolution left19 factorial step11 := mul(3628800, 11)

Exp convolution left19 factorial step11 = 39916800

Exp convolution left19 factorial step12 := mul(39916800, 12)

Exp convolution left19 factorial step12 = 479001600

Exp convolution left19 factorial step13 := mul(479001600, 13)

Exp convolution left19 factorial step13 = 6227020800

Exp convolution left19 factorial step14 := mul(6227020800, 14)

Exp convolution left19 factorial step14 = 87178291200

Exp convolution left19 factorial step15 := mul(87178291200, 15)

Exp convolution left19 factorial step15 = 1307674368000

Exp convolution left19 factorial step16 := mul(1307674368000, 16)

Exp convolution left19 factorial step16 = 20922789888000

Exp convolution left19 factorial step17 := mul(20922789888000, 17)

Exp convolution left19 factorial step17 = 355687428096000

Exp convolution left19 factorial step18 := mul(355687428096000, 18)

Exp convolution left19 factorial step18 = 6402373705728000

Exp convolution left19 factorial step19 := mul(6402373705728000, 19)

Exp convolution left19 factorial step19 = 121645100408832000

source roles = [0]

derived = [1]

Exp convolution denominator19 := mul(121645100408832000, 1)

Exp convolution denominator19 = 121645100408832000

Exp convolution coefficient term19 := div(5242880000000000000000000/13248496640331026125580781, 121645100408832000)

Exp convolution coefficient term19 = 640000000000000000/196730310556535776929773039037663801

Exp complete declared-degree convolution := sum(-41209797661291758429/12132755312575326542353091425992704000, 93446253200208069/1451286520642981643822140122726400, -1907066391840981/3298378456006776463232136642560, 1441471195647/440959686631921987063119872, -16343210835/1252726382477051099611136, 555891525/14235527073602853404672, -14706125/161767353109123334144, 214375/1272645260473872384, -21875/86771267759582208, 15625/50825732251738752, -78125/254706226397918064, 390625/1560075636687248142, -15625000/93817275788055876903, 625000000/6985122624583433016687, -25000000000/653426470972395688560993, 1000000000000/78589383736043590542381249, -10000000000000/3150719838872293039017284619, 400000000000000/715786261576532754954926751171, -16000000000000000/258268697472478045856009479581609, 640000000000000000/196730310556535776929773039037663801)

Exp complete declared-degree convolution = -1/51676388762462995371436759840422682365878499503552553575761575936000

Exp ORIGINAL arguments sum := sum(20/21, -21/22)

Exp ORIGINAL arguments sum = -1/462

(-1/462)^19

Exp sum argument declared power = -1/424812742878964726690543661011206668804126550786048

Exp sum argument factorial step1 := mul(1, 1)

Exp sum argument factorial step1 = 1

Exp sum argument factorial step2 := mul(1, 2)

Exp sum argument factorial step2 = 2

Exp sum argument factorial step3 := mul(2, 3)

Exp sum argument factorial step3 = 6

Exp sum argument factorial step4 := mul(6, 4)

Exp sum argument factorial step4 = 24

Exp sum argument factorial step5 := mul(24, 5)

Exp sum argument factorial step5 = 120

Exp sum argument factorial step6 := mul(120, 6)

Exp sum argument factorial step6 = 720

Exp sum argument factorial step7 := mul(720, 7)

Exp sum argument factorial step7 = 5040

Exp sum argument factorial step8 := mul(5040, 8)

Exp sum argument factorial step8 = 40320

Exp sum argument factorial step9 := mul(40320, 9)

Exp sum argument factorial step9 = 362880

Exp sum argument factorial step10 := mul(362880, 10)

Exp sum argument factorial step10 = 3628800

Exp sum argument factorial step11 := mul(3628800, 11)

Exp sum argument factorial step11 = 39916800

Exp sum argument factorial step12 := mul(39916800, 12)

Exp sum argument factorial step12 = 479001600

Exp sum argument factorial step13 := mul(479001600, 13)

Exp sum argument factorial step13 = 6227020800

Exp sum argument factorial step14 := mul(6227020800, 14)

Exp sum argument factorial step14 = 87178291200

Exp sum argument factorial step15 := mul(87178291200, 15)

Exp sum argument factorial step15 = 1307674368000

Exp sum argument factorial step16 := mul(1307674368000, 16)

Exp sum argument factorial step16 = 20922789888000

Exp sum argument factorial step17 := mul(20922789888000, 17)

Exp sum argument factorial step17 = 355687428096000

Exp sum argument factorial step18 := mul(355687428096000, 18)

Exp sum argument factorial step18 = 6402373705728000

Exp sum argument factorial step19 := mul(6402373705728000, 19)

Exp sum argument factorial step19 = 121645100408832000

Exp sum argument coefficient := div(-1/424812742878964726690543661011206668804126550786048, 121645100408832000)

Exp sum argument coefficient = -1/51676388762462995371436759840422682365878499503552553575761575936000

source roles = [[20/21, -21/22], a_n=1/n! for EVERY n>=0]

derived = [coefficient ratio=1/(n+1), for EVERY fixed real z,term absolute ratio=|z|/(n+1)->0, absolute convergence and real-valued E(z)]

source roles = [[20/21, -21/22, 19], E(x),E(y) absolutely convergent]

derived = [for EVERY n,sum_k x^k*y^(n-k)/(k!*(n-k)!)=(x+y)^n/n!, E(x)E(y)=E(x+y)]

Reverse checks

• S508 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S507 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S506 · premise_and_result_audit — Recompute Exp sum argument coefficient with exact rational arithmetic, not rounded decimals.
• S505 · premise_and_result_audit — Recompute Exp sum argument factorial step19 with exact rational arithmetic, not rounded decimals.
• S504 · premise_and_result_audit — Recompute Exp sum argument factorial step18 with exact rational arithmetic, not rounded decimals.
• S503 · premise_and_result_audit — Recompute Exp sum argument factorial step17 with exact rational arithmetic, not rounded decimals.
• S502 · premise_and_result_audit — Recompute Exp sum argument factorial step16 with exact rational arithmetic, not rounded decimals.
• S501 · premise_and_result_audit — Recompute Exp sum argument factorial step15 with exact rational arithmetic, not rounded decimals.
• S500 · premise_and_result_audit — Recompute Exp sum argument factorial step14 with exact rational arithmetic, not rounded decimals.
• S499 · premise_and_result_audit — Recompute Exp sum argument factorial step13 with exact rational arithmetic, not rounded decimals.
• S498 · premise_and_result_audit — Recompute Exp sum argument factorial step12 with exact rational arithmetic, not rounded decimals.
• S497 · premise_and_result_audit — Recompute Exp sum argument factorial step11 with exact rational arithmetic, not rounded decimals.
• S496 · premise_and_result_audit — Recompute Exp sum argument factorial step10 with exact rational arithmetic, not rounded decimals.
• S495 · premise_and_result_audit — Recompute Exp sum argument factorial step9 with exact rational arithmetic, not rounded decimals.
• S494 · premise_and_result_audit — Recompute Exp sum argument factorial step8 with exact rational arithmetic, not rounded decimals.
• S493 · premise_and_result_audit — Recompute Exp sum argument factorial step7 with exact rational arithmetic, not rounded decimals.
• S492 · premise_and_result_audit — Recompute Exp sum argument factorial step6 with exact rational arithmetic, not rounded decimals.
• S491 · premise_and_result_audit — Recompute Exp sum argument factorial step5 with exact rational arithmetic, not rounded decimals.
• S490 · premise_and_result_audit — Recompute Exp sum argument factorial step4 with exact rational arithmetic, not rounded decimals.
• S489 · premise_and_result_audit — Recompute Exp sum argument factorial step3 with exact rational arithmetic, not rounded decimals.
• S488 · premise_and_result_audit — Recompute Exp sum argument factorial step2 with exact rational arithmetic, not rounded decimals.
• S487 · premise_and_result_audit — Recompute Exp sum argument factorial step1 with exact rational arithmetic, not rounded decimals.
• S486 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S485 · premise_and_result_audit — Recompute Exp ORIGINAL arguments sum with exact rational arithmetic, not rounded decimals.
• S484 · premise_and_result_audit — Recompute Exp complete declared-degree convolution with exact rational arithmetic, not rounded decimals.
• S483 · premise_and_result_audit — Recompute Exp convolution coefficient term19 with exact rational arithmetic, not rounded decimals.
• S482 · premise_and_result_audit — Recompute Exp convolution denominator19 with exact rational arithmetic, not rounded decimals.
• S481 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S480 · premise_and_result_audit — Recompute Exp convolution left19 factorial step19 with exact rational arithmetic, not rounded decimals.
• S479 · premise_and_result_audit — Recompute Exp convolution left19 factorial step18 with exact rational arithmetic, not rounded decimals.
• S478 · premise_and_result_audit — Recompute Exp convolution left19 factorial step17 with exact rational arithmetic, not rounded decimals.
• S477 · premise_and_result_audit — Recompute Exp convolution left19 factorial step16 with exact rational arithmetic, not rounded decimals.
• S476 · premise_and_result_audit — Recompute Exp convolution left19 factorial step15 with exact rational arithmetic, not rounded decimals.
• S475 · premise_and_result_audit — Recompute Exp convolution left19 factorial step14 with exact rational arithmetic, not rounded decimals.
• S474 · premise_and_result_audit — Recompute Exp convolution left19 factorial step13 with exact rational arithmetic, not rounded decimals.
• S473 · premise_and_result_audit — Recompute Exp convolution left19 factorial step12 with exact rational arithmetic, not rounded decimals.
• S472 · premise_and_result_audit — Recompute Exp convolution left19 factorial step11 with exact rational arithmetic, not rounded decimals.
• S471 · premise_and_result_audit — Recompute Exp convolution left19 factorial step10 with exact rational arithmetic, not rounded decimals.
• S470 · premise_and_result_audit — Recompute Exp convolution left19 factorial step9 with exact rational arithmetic, not rounded decimals.
• S469 · premise_and_result_audit — Recompute Exp convolution left19 factorial step8 with exact rational arithmetic, not rounded decimals.
• S468 · premise_and_result_audit — Recompute Exp convolution left19 factorial step7 with exact rational arithmetic, not rounded decimals.
• S467 · premise_and_result_audit — Recompute Exp convolution left19 factorial step6 with exact rational arithmetic, not rounded decimals.
• S466 · premise_and_result_audit — Recompute Exp convolution left19 factorial step5 with exact rational arithmetic, not rounded decimals.
• S465 · premise_and_result_audit — Recompute Exp convolution left19 factorial step4 with exact rational arithmetic, not rounded decimals.
• S464 · premise_and_result_audit — Recompute Exp convolution left19 factorial step3 with exact rational arithmetic, not rounded decimals.
• S463 · premise_and_result_audit — Recompute Exp convolution left19 factorial step2 with exact rational arithmetic, not rounded decimals.
• S462 · premise_and_result_audit — Recompute Exp convolution left19 factorial step1 with exact rational arithmetic, not rounded decimals.
• S461 · premise_and_result_audit — Recompute Exp convolution numerator19 with exact rational arithmetic, not rounded decimals.
• S460 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S459 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S458 · premise_and_result_audit — Recompute Exp convolution coefficient term18 with exact rational arithmetic, not rounded decimals.
• S457 · premise_and_result_audit — Recompute Exp convolution denominator18 with exact rational arithmetic, not rounded decimals.
• S456 · premise_and_result_audit — Recompute Exp convolution right18 factorial step1 with exact rational arithmetic, not rounded decimals.
• S455 · premise_and_result_audit — Recompute Exp convolution left18 factorial step18 with exact rational arithmetic, not rounded decimals.
• S454 · premise_and_result_audit — Recompute Exp convolution left18 factorial step17 with exact rational arithmetic, not rounded decimals.
• S453 · premise_and_result_audit — Recompute Exp convolution left18 factorial step16 with exact rational arithmetic, not rounded decimals.
• S452 · premise_and_result_audit — Recompute Exp convolution left18 factorial step15 with exact rational arithmetic, not rounded decimals.
• S451 · premise_and_result_audit — Recompute Exp convolution left18 factorial step14 with exact rational arithmetic, not rounded decimals.
• S450 · premise_and_result_audit — Recompute Exp convolution left18 factorial step13 with exact rational arithmetic, not rounded decimals.
• S449 · premise_and_result_audit — Recompute Exp convolution left18 factorial step12 with exact rational arithmetic, not rounded decimals.
• S448 · premise_and_result_audit — Recompute Exp convolution left18 factorial step11 with exact rational arithmetic, not rounded decimals.
• S447 · premise_and_result_audit — Recompute Exp convolution left18 factorial step10 with exact rational arithmetic, not rounded decimals.
• S446 · premise_and_result_audit — Recompute Exp convolution left18 factorial step9 with exact rational arithmetic, not rounded decimals.
• S445 · premise_and_result_audit — Recompute Exp convolution left18 factorial step8 with exact rational arithmetic, not rounded decimals.
• S444 · premise_and_result_audit — Recompute Exp convolution left18 factorial step7 with exact rational arithmetic, not rounded decimals.
• S443 · premise_and_result_audit — Recompute Exp convolution left18 factorial step6 with exact rational arithmetic, not rounded decimals.
• S442 · premise_and_result_audit — Recompute Exp convolution left18 factorial step5 with exact rational arithmetic, not rounded decimals.
• S441 · premise_and_result_audit — Recompute Exp convolution left18 factorial step4 with exact rational arithmetic, not rounded decimals.
• S440 · premise_and_result_audit — Recompute Exp convolution left18 factorial step3 with exact rational arithmetic, not rounded decimals.
• S439 · premise_and_result_audit — Recompute Exp convolution left18 factorial step2 with exact rational arithmetic, not rounded decimals.
• S438 · premise_and_result_audit — Recompute Exp convolution left18 factorial step1 with exact rational arithmetic, not rounded decimals.
• S437 · premise_and_result_audit — Recompute Exp convolution numerator18 with exact rational arithmetic, not rounded decimals.
• S436 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S435 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S434 · premise_and_result_audit — Recompute Exp convolution coefficient term17 with exact rational arithmetic, not rounded decimals.
• S433 · premise_and_result_audit — Recompute Exp convolution denominator17 with exact rational arithmetic, not rounded decimals.
• S432 · premise_and_result_audit — Recompute Exp convolution right17 factorial step2 with exact rational arithmetic, not rounded decimals.
• S431 · premise_and_result_audit — Recompute Exp convolution right17 factorial step1 with exact rational arithmetic, not rounded decimals.
• S430 · premise_and_result_audit — Recompute Exp convolution left17 factorial step17 with exact rational arithmetic, not rounded decimals.
• S429 · premise_and_result_audit — Recompute Exp convolution left17 factorial step16 with exact rational arithmetic, not rounded decimals.
• S428 · premise_and_result_audit — Recompute Exp convolution left17 factorial step15 with exact rational arithmetic, not rounded decimals.
• S427 · premise_and_result_audit — Recompute Exp convolution left17 factorial step14 with exact rational arithmetic, not rounded decimals.
• S426 · premise_and_result_audit — Recompute Exp convolution left17 factorial step13 with exact rational arithmetic, not rounded decimals.
• S425 · premise_and_result_audit — Recompute Exp convolution left17 factorial step12 with exact rational arithmetic, not rounded decimals.
• S424 · premise_and_result_audit — Recompute Exp convolution left17 factorial step11 with exact rational arithmetic, not rounded decimals.
• S423 · premise_and_result_audit — Recompute Exp convolution left17 factorial step10 with exact rational arithmetic, not rounded decimals.
• S422 · premise_and_result_audit — Recompute Exp convolution left17 factorial step9 with exact rational arithmetic, not rounded decimals.
• S421 · premise_and_result_audit — Recompute Exp convolution left17 factorial step8 with exact rational arithmetic, not rounded decimals.
• S420 · premise_and_result_audit — Recompute Exp convolution left17 factorial step7 with exact rational arithmetic, not rounded decimals.
• S419 · premise_and_result_audit — Recompute Exp convolution left17 factorial step6 with exact rational arithmetic, not rounded decimals.
• S418 · premise_and_result_audit — Recompute Exp convolution left17 factorial step5 with exact rational arithmetic, not rounded decimals.
• S417 · premise_and_result_audit — Recompute Exp convolution left17 factorial step4 with exact rational arithmetic, not rounded decimals.
• S416 · premise_and_result_audit — Recompute Exp convolution left17 factorial step3 with exact rational arithmetic, not rounded decimals.
• S415 · premise_and_result_audit — Recompute Exp convolution left17 factorial step2 with exact rational arithmetic, not rounded decimals.
• S414 · premise_and_result_audit — Recompute Exp convolution left17 factorial step1 with exact rational arithmetic, not rounded decimals.
• S413 · premise_and_result_audit — Recompute Exp convolution numerator17 with exact rational arithmetic, not rounded decimals.
• S412 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S411 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S410 · premise_and_result_audit — Recompute Exp convolution coefficient term16 with exact rational arithmetic, not rounded decimals.
• S409 · premise_and_result_audit — Recompute Exp convolution denominator16 with exact rational arithmetic, not rounded decimals.
• S408 · premise_and_result_audit — Recompute Exp convolution right16 factorial step3 with exact rational arithmetic, not rounded decimals.
• S407 · premise_and_result_audit — Recompute Exp convolution right16 factorial step2 with exact rational arithmetic, not rounded decimals.
• S406 · premise_and_result_audit — Recompute Exp convolution right16 factorial step1 with exact rational arithmetic, not rounded decimals.
• S405 · premise_and_result_audit — Recompute Exp convolution left16 factorial step16 with exact rational arithmetic, not rounded decimals.
• S404 · premise_and_result_audit — Recompute Exp convolution left16 factorial step15 with exact rational arithmetic, not rounded decimals.
• S403 · premise_and_result_audit — Recompute Exp convolution left16 factorial step14 with exact rational arithmetic, not rounded decimals.
• S402 · premise_and_result_audit — Recompute Exp convolution left16 factorial step13 with exact rational arithmetic, not rounded decimals.
• S401 · premise_and_result_audit — Recompute Exp convolution left16 factorial step12 with exact rational arithmetic, not rounded decimals.
• S400 · premise_and_result_audit — Recompute Exp convolution left16 factorial step11 with exact rational arithmetic, not rounded decimals.
• S399 · premise_and_result_audit — Recompute Exp convolution left16 factorial step10 with exact rational arithmetic, not rounded decimals.
• S398 · premise_and_result_audit — Recompute Exp convolution left16 factorial step9 with exact rational arithmetic, not rounded decimals.
• S397 · premise_and_result_audit — Recompute Exp convolution left16 factorial step8 with exact rational arithmetic, not rounded decimals.
• S396 · premise_and_result_audit — Recompute Exp convolution left16 factorial step7 with exact rational arithmetic, not rounded decimals.
• S395 · premise_and_result_audit — Recompute Exp convolution left16 factorial step6 with exact rational arithmetic, not rounded decimals.
• S394 · premise_and_result_audit — Recompute Exp convolution left16 factorial step5 with exact rational arithmetic, not rounded decimals.
• S393 · premise_and_result_audit — Recompute Exp convolution left16 factorial step4 with exact rational arithmetic, not rounded decimals.
• S392 · premise_and_result_audit — Recompute Exp convolution left16 factorial step3 with exact rational arithmetic, not rounded decimals.
• S391 · premise_and_result_audit — Recompute Exp convolution left16 factorial step2 with exact rational arithmetic, not rounded decimals.
• S390 · premise_and_result_audit — Recompute Exp convolution left16 factorial step1 with exact rational arithmetic, not rounded decimals.
• S389 · premise_and_result_audit — Recompute Exp convolution numerator16 with exact rational arithmetic, not rounded decimals.
• S388 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S387 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S386 · premise_and_result_audit — Recompute Exp convolution coefficient term15 with exact rational arithmetic, not rounded decimals.
• S385 · premise_and_result_audit — Recompute Exp convolution denominator15 with exact rational arithmetic, not rounded decimals.
• S384 · premise_and_result_audit — Recompute Exp convolution right15 factorial step4 with exact rational arithmetic, not rounded decimals.
• S383 · premise_and_result_audit — Recompute Exp convolution right15 factorial step3 with exact rational arithmetic, not rounded decimals.
• S382 · premise_and_result_audit — Recompute Exp convolution right15 factorial step2 with exact rational arithmetic, not rounded decimals.
• S381 · premise_and_result_audit — Recompute Exp convolution right15 factorial step1 with exact rational arithmetic, not rounded decimals.
• S380 · premise_and_result_audit — Recompute Exp convolution left15 factorial step15 with exact rational arithmetic, not rounded decimals.
• S379 · premise_and_result_audit — Recompute Exp convolution left15 factorial step14 with exact rational arithmetic, not rounded decimals.
• S378 · premise_and_result_audit — Recompute Exp convolution left15 factorial step13 with exact rational arithmetic, not rounded decimals.
• S377 · premise_and_result_audit — Recompute Exp convolution left15 factorial step12 with exact rational arithmetic, not rounded decimals.
• S376 · premise_and_result_audit — Recompute Exp convolution left15 factorial step11 with exact rational arithmetic, not rounded decimals.
• S375 · premise_and_result_audit — Recompute Exp convolution left15 factorial step10 with exact rational arithmetic, not rounded decimals.
• S374 · premise_and_result_audit — Recompute Exp convolution left15 factorial step9 with exact rational arithmetic, not rounded decimals.
• S373 · premise_and_result_audit — Recompute Exp convolution left15 factorial step8 with exact rational arithmetic, not rounded decimals.
• S372 · premise_and_result_audit — Recompute Exp convolution left15 factorial step7 with exact rational arithmetic, not rounded decimals.
• S371 · premise_and_result_audit — Recompute Exp convolution left15 factorial step6 with exact rational arithmetic, not rounded decimals.
• S370 · premise_and_result_audit — Recompute Exp convolution left15 factorial step5 with exact rational arithmetic, not rounded decimals.
• S369 · premise_and_result_audit — Recompute Exp convolution left15 factorial step4 with exact rational arithmetic, not rounded decimals.
• S368 · premise_and_result_audit — Recompute Exp convolution left15 factorial step3 with exact rational arithmetic, not rounded decimals.
• S367 · premise_and_result_audit — Recompute Exp convolution left15 factorial step2 with exact rational arithmetic, not rounded decimals.
• S366 · premise_and_result_audit — Recompute Exp convolution left15 factorial step1 with exact rational arithmetic, not rounded decimals.
• S365 · premise_and_result_audit — Recompute Exp convolution numerator15 with exact rational arithmetic, not rounded decimals.
• S364 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S363 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S362 · premise_and_result_audit — Recompute Exp convolution coefficient term14 with exact rational arithmetic, not rounded decimals.
• S361 · premise_and_result_audit — Recompute Exp convolution denominator14 with exact rational arithmetic, not rounded decimals.
• S360 · premise_and_result_audit — Recompute Exp convolution right14 factorial step5 with exact rational arithmetic, not rounded decimals.
• S359 · premise_and_result_audit — Recompute Exp convolution right14 factorial step4 with exact rational arithmetic, not rounded decimals.
• S358 · premise_and_result_audit — Recompute Exp convolution right14 factorial step3 with exact rational arithmetic, not rounded decimals.
• S357 · premise_and_result_audit — Recompute Exp convolution right14 factorial step2 with exact rational arithmetic, not rounded decimals.
• S356 · premise_and_result_audit — Recompute Exp convolution right14 factorial step1 with exact rational arithmetic, not rounded decimals.
• S355 · premise_and_result_audit — Recompute Exp convolution left14 factorial step14 with exact rational arithmetic, not rounded decimals.
• S354 · premise_and_result_audit — Recompute Exp convolution left14 factorial step13 with exact rational arithmetic, not rounded decimals.
• S353 · premise_and_result_audit — Recompute Exp convolution left14 factorial step12 with exact rational arithmetic, not rounded decimals.
• S352 · premise_and_result_audit — Recompute Exp convolution left14 factorial step11 with exact rational arithmetic, not rounded decimals.
• S351 · premise_and_result_audit — Recompute Exp convolution left14 factorial step10 with exact rational arithmetic, not rounded decimals.
• S350 · premise_and_result_audit — Recompute Exp convolution left14 factorial step9 with exact rational arithmetic, not rounded decimals.
• S349 · premise_and_result_audit — Recompute Exp convolution left14 factorial step8 with exact rational arithmetic, not rounded decimals.
• S348 · premise_and_result_audit — Recompute Exp convolution left14 factorial step7 with exact rational arithmetic, not rounded decimals.
• S347 · premise_and_result_audit — Recompute Exp convolution left14 factorial step6 with exact rational arithmetic, not rounded decimals.
• S346 · premise_and_result_audit — Recompute Exp convolution left14 factorial step5 with exact rational arithmetic, not rounded decimals.
• S345 · premise_and_result_audit — Recompute Exp convolution left14 factorial step4 with exact rational arithmetic, not rounded decimals.
• S344 · premise_and_result_audit — Recompute Exp convolution left14 factorial step3 with exact rational arithmetic, not rounded decimals.
• S343 · premise_and_result_audit — Recompute Exp convolution left14 factorial step2 with exact rational arithmetic, not rounded decimals.
• S342 · premise_and_result_audit — Recompute Exp convolution left14 factorial step1 with exact rational arithmetic, not rounded decimals.
• S341 · premise_and_result_audit — Recompute Exp convolution numerator14 with exact rational arithmetic, not rounded decimals.
• S340 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S339 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S338 · premise_and_result_audit — Recompute Exp convolution coefficient term13 with exact rational arithmetic, not rounded decimals.
• S337 · premise_and_result_audit — Recompute Exp convolution denominator13 with exact rational arithmetic, not rounded decimals.
• S336 · premise_and_result_audit — Recompute Exp convolution right13 factorial step6 with exact rational arithmetic, not rounded decimals.
• S335 · premise_and_result_audit — Recompute Exp convolution right13 factorial step5 with exact rational arithmetic, not rounded decimals.
• S334 · premise_and_result_audit — Recompute Exp convolution right13 factorial step4 with exact rational arithmetic, not rounded decimals.
• S333 · premise_and_result_audit — Recompute Exp convolution right13 factorial step3 with exact rational arithmetic, not rounded decimals.
• S332 · premise_and_result_audit — Recompute Exp convolution right13 factorial step2 with exact rational arithmetic, not rounded decimals.
• S331 · premise_and_result_audit — Recompute Exp convolution right13 factorial step1 with exact rational arithmetic, not rounded decimals.
• S330 · premise_and_result_audit — Recompute Exp convolution left13 factorial step13 with exact rational arithmetic, not rounded decimals.
• S329 · premise_and_result_audit — Recompute Exp convolution left13 factorial step12 with exact rational arithmetic, not rounded decimals.
• S328 · premise_and_result_audit — Recompute Exp convolution left13 factorial step11 with exact rational arithmetic, not rounded decimals.
• S327 · premise_and_result_audit — Recompute Exp convolution left13 factorial step10 with exact rational arithmetic, not rounded decimals.
• S326 · premise_and_result_audit — Recompute Exp convolution left13 factorial step9 with exact rational arithmetic, not rounded decimals.
• S325 · premise_and_result_audit — Recompute Exp convolution left13 factorial step8 with exact rational arithmetic, not rounded decimals.
• S324 · premise_and_result_audit — Recompute Exp convolution left13 factorial step7 with exact rational arithmetic, not rounded decimals.
• S323 · premise_and_result_audit — Recompute Exp convolution left13 factorial step6 with exact rational arithmetic, not rounded decimals.
• S322 · premise_and_result_audit — Recompute Exp convolution left13 factorial step5 with exact rational arithmetic, not rounded decimals.
• S321 · premise_and_result_audit — Recompute Exp convolution left13 factorial step4 with exact rational arithmetic, not rounded decimals.
• S320 · premise_and_result_audit — Recompute Exp convolution left13 factorial step3 with exact rational arithmetic, not rounded decimals.
• S319 · premise_and_result_audit — Recompute Exp convolution left13 factorial step2 with exact rational arithmetic, not rounded decimals.
• S318 · premise_and_result_audit — Recompute Exp convolution left13 factorial step1 with exact rational arithmetic, not rounded decimals.
• S317 · premise_and_result_audit — Recompute Exp convolution numerator13 with exact rational arithmetic, not rounded decimals.
• S316 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S315 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S314 · premise_and_result_audit — Recompute Exp convolution coefficient term12 with exact rational arithmetic, not rounded decimals.
• S313 · premise_and_result_audit — Recompute Exp convolution denominator12 with exact rational arithmetic, not rounded decimals.
• S312 · premise_and_result_audit — Recompute Exp convolution right12 factorial step7 with exact rational arithmetic, not rounded decimals.
• S311 · premise_and_result_audit — Recompute Exp convolution right12 factorial step6 with exact rational arithmetic, not rounded decimals.
• S310 · premise_and_result_audit — Recompute Exp convolution right12 factorial step5 with exact rational arithmetic, not rounded decimals.
• S309 · premise_and_result_audit — Recompute Exp convolution right12 factorial step4 with exact rational arithmetic, not rounded decimals.
• S308 · premise_and_result_audit — Recompute Exp convolution right12 factorial step3 with exact rational arithmetic, not rounded decimals.
• S307 · premise_and_result_audit — Recompute Exp convolution right12 factorial step2 with exact rational arithmetic, not rounded decimals.
• S306 · premise_and_result_audit — Recompute Exp convolution right12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S305 · premise_and_result_audit — Recompute Exp convolution left12 factorial step12 with exact rational arithmetic, not rounded decimals.
• S304 · premise_and_result_audit — Recompute Exp convolution left12 factorial step11 with exact rational arithmetic, not rounded decimals.
• S303 · premise_and_result_audit — Recompute Exp convolution left12 factorial step10 with exact rational arithmetic, not rounded decimals.
• S302 · premise_and_result_audit — Recompute Exp convolution left12 factorial step9 with exact rational arithmetic, not rounded decimals.
• S301 · premise_and_result_audit — Recompute Exp convolution left12 factorial step8 with exact rational arithmetic, not rounded decimals.
• S300 · premise_and_result_audit — Recompute Exp convolution left12 factorial step7 with exact rational arithmetic, not rounded decimals.
• S299 · premise_and_result_audit — Recompute Exp convolution left12 factorial step6 with exact rational arithmetic, not rounded decimals.
• S298 · premise_and_result_audit — Recompute Exp convolution left12 factorial step5 with exact rational arithmetic, not rounded decimals.
• S297 · premise_and_result_audit — Recompute Exp convolution left12 factorial step4 with exact rational arithmetic, not rounded decimals.
• S296 · premise_and_result_audit — Recompute Exp convolution left12 factorial step3 with exact rational arithmetic, not rounded decimals.
• S295 · premise_and_result_audit — Recompute Exp convolution left12 factorial step2 with exact rational arithmetic, not rounded decimals.
• S294 · premise_and_result_audit — Recompute Exp convolution left12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S293 · premise_and_result_audit — Recompute Exp convolution numerator12 with exact rational arithmetic, not rounded decimals.
• S292 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S291 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S290 · premise_and_result_audit — Recompute Exp convolution coefficient term11 with exact rational arithmetic, not rounded decimals.
• S289 · premise_and_result_audit — Recompute Exp convolution denominator11 with exact rational arithmetic, not rounded decimals.
• S288 · premise_and_result_audit — Recompute Exp convolution right11 factorial step8 with exact rational arithmetic, not rounded decimals.
• S287 · premise_and_result_audit — Recompute Exp convolution right11 factorial step7 with exact rational arithmetic, not rounded decimals.
• S286 · premise_and_result_audit — Recompute Exp convolution right11 factorial step6 with exact rational arithmetic, not rounded decimals.
• S285 · premise_and_result_audit — Recompute Exp convolution right11 factorial step5 with exact rational arithmetic, not rounded decimals.
• S284 · premise_and_result_audit — Recompute Exp convolution right11 factorial step4 with exact rational arithmetic, not rounded decimals.
• S283 · premise_and_result_audit — Recompute Exp convolution right11 factorial step3 with exact rational arithmetic, not rounded decimals.
• S282 · premise_and_result_audit — Recompute Exp convolution right11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S281 · premise_and_result_audit — Recompute Exp convolution right11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S280 · premise_and_result_audit — Recompute Exp convolution left11 factorial step11 with exact rational arithmetic, not rounded decimals.
• S279 · premise_and_result_audit — Recompute Exp convolution left11 factorial step10 with exact rational arithmetic, not rounded decimals.
• S278 · premise_and_result_audit — Recompute Exp convolution left11 factorial step9 with exact rational arithmetic, not rounded decimals.
• S277 · premise_and_result_audit — Recompute Exp convolution left11 factorial step8 with exact rational arithmetic, not rounded decimals.
• S276 · premise_and_result_audit — Recompute Exp convolution left11 factorial step7 with exact rational arithmetic, not rounded decimals.
• S275 · premise_and_result_audit — Recompute Exp convolution left11 factorial step6 with exact rational arithmetic, not rounded decimals.
• S274 · premise_and_result_audit — Recompute Exp convolution left11 factorial step5 with exact rational arithmetic, not rounded decimals.
• S273 · premise_and_result_audit — Recompute Exp convolution left11 factorial step4 with exact rational arithmetic, not rounded decimals.
• S272 · premise_and_result_audit — Recompute Exp convolution left11 factorial step3 with exact rational arithmetic, not rounded decimals.
• S271 · premise_and_result_audit — Recompute Exp convolution left11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S270 · premise_and_result_audit — Recompute Exp convolution left11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S269 · premise_and_result_audit — Recompute Exp convolution numerator11 with exact rational arithmetic, not rounded decimals.
• S268 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S267 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S266 · premise_and_result_audit — Recompute Exp convolution coefficient term10 with exact rational arithmetic, not rounded decimals.
• S265 · premise_and_result_audit — Recompute Exp convolution denominator10 with exact rational arithmetic, not rounded decimals.
• S264 · premise_and_result_audit — Recompute Exp convolution right10 factorial step9 with exact rational arithmetic, not rounded decimals.
• S263 · premise_and_result_audit — Recompute Exp convolution right10 factorial step8 with exact rational arithmetic, not rounded decimals.
• S262 · premise_and_result_audit — Recompute Exp convolution right10 factorial step7 with exact rational arithmetic, not rounded decimals.
• S261 · premise_and_result_audit — Recompute Exp convolution right10 factorial step6 with exact rational arithmetic, not rounded decimals.
• S260 · premise_and_result_audit — Recompute Exp convolution right10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S259 · premise_and_result_audit — Recompute Exp convolution right10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S258 · premise_and_result_audit — Recompute Exp convolution right10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S257 · premise_and_result_audit — Recompute Exp convolution right10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S256 · premise_and_result_audit — Recompute Exp convolution right10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S255 · premise_and_result_audit — Recompute Exp convolution left10 factorial step10 with exact rational arithmetic, not rounded decimals.
• S254 · premise_and_result_audit — Recompute Exp convolution left10 factorial step9 with exact rational arithmetic, not rounded decimals.
• S253 · premise_and_result_audit — Recompute Exp convolution left10 factorial step8 with exact rational arithmetic, not rounded decimals.
• S252 · premise_and_result_audit — Recompute Exp convolution left10 factorial step7 with exact rational arithmetic, not rounded decimals.
• S251 · premise_and_result_audit — Recompute Exp convolution left10 factorial step6 with exact rational arithmetic, not rounded decimals.
• S250 · premise_and_result_audit — Recompute Exp convolution left10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S249 · premise_and_result_audit — Recompute Exp convolution left10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S248 · premise_and_result_audit — Recompute Exp convolution left10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S247 · premise_and_result_audit — Recompute Exp convolution left10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S246 · premise_and_result_audit — Recompute Exp convolution left10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S245 · premise_and_result_audit — Recompute Exp convolution numerator10 with exact rational arithmetic, not rounded decimals.
• S244 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S243 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S242 · premise_and_result_audit — Recompute Exp convolution coefficient term9 with exact rational arithmetic, not rounded decimals.
• S241 · premise_and_result_audit — Recompute Exp convolution denominator9 with exact rational arithmetic, not rounded decimals.
• S240 · premise_and_result_audit — Recompute Exp convolution right9 factorial step10 with exact rational arithmetic, not rounded decimals.
• S239 · premise_and_result_audit — Recompute Exp convolution right9 factorial step9 with exact rational arithmetic, not rounded decimals.
• S238 · premise_and_result_audit — Recompute Exp convolution right9 factorial step8 with exact rational arithmetic, not rounded decimals.
• S237 · premise_and_result_audit — Recompute Exp convolution right9 factorial step7 with exact rational arithmetic, not rounded decimals.
• S236 · premise_and_result_audit — Recompute Exp convolution right9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S235 · premise_and_result_audit — Recompute Exp convolution right9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S234 · premise_and_result_audit — Recompute Exp convolution right9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S233 · premise_and_result_audit — Recompute Exp convolution right9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S232 · premise_and_result_audit — Recompute Exp convolution right9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S231 · premise_and_result_audit — Recompute Exp convolution right9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S230 · premise_and_result_audit — Recompute Exp convolution left9 factorial step9 with exact rational arithmetic, not rounded decimals.
• S229 · premise_and_result_audit — Recompute Exp convolution left9 factorial step8 with exact rational arithmetic, not rounded decimals.
• S228 · premise_and_result_audit — Recompute Exp convolution left9 factorial step7 with exact rational arithmetic, not rounded decimals.
• S227 · premise_and_result_audit — Recompute Exp convolution left9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S226 · premise_and_result_audit — Recompute Exp convolution left9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S225 · premise_and_result_audit — Recompute Exp convolution left9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S224 · premise_and_result_audit — Recompute Exp convolution left9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S223 · premise_and_result_audit — Recompute Exp convolution left9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S222 · premise_and_result_audit — Recompute Exp convolution left9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S221 · premise_and_result_audit — Recompute Exp convolution numerator9 with exact rational arithmetic, not rounded decimals.
• S220 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S219 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S218 · premise_and_result_audit — Recompute Exp convolution coefficient term8 with exact rational arithmetic, not rounded decimals.
• S217 · premise_and_result_audit — Recompute Exp convolution denominator8 with exact rational arithmetic, not rounded decimals.
• S216 · premise_and_result_audit — Recompute Exp convolution right8 factorial step11 with exact rational arithmetic, not rounded decimals.
• S215 · premise_and_result_audit — Recompute Exp convolution right8 factorial step10 with exact rational arithmetic, not rounded decimals.
• S214 · premise_and_result_audit — Recompute Exp convolution right8 factorial step9 with exact rational arithmetic, not rounded decimals.
• S213 · premise_and_result_audit — Recompute Exp convolution right8 factorial step8 with exact rational arithmetic, not rounded decimals.
• S212 · premise_and_result_audit — Recompute Exp convolution right8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S211 · premise_and_result_audit — Recompute Exp convolution right8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S210 · premise_and_result_audit — Recompute Exp convolution right8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S209 · premise_and_result_audit — Recompute Exp convolution right8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S208 · premise_and_result_audit — Recompute Exp convolution right8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S207 · premise_and_result_audit — Recompute Exp convolution right8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S206 · premise_and_result_audit — Recompute Exp convolution right8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S205 · premise_and_result_audit — Recompute Exp convolution left8 factorial step8 with exact rational arithmetic, not rounded decimals.
• S204 · premise_and_result_audit — Recompute Exp convolution left8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S203 · premise_and_result_audit — Recompute Exp convolution left8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S202 · premise_and_result_audit — Recompute Exp convolution left8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S201 · premise_and_result_audit — Recompute Exp convolution left8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S200 · premise_and_result_audit — Recompute Exp convolution left8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S199 · premise_and_result_audit — Recompute Exp convolution left8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S198 · premise_and_result_audit — Recompute Exp convolution left8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S197 · premise_and_result_audit — Recompute Exp convolution numerator8 with exact rational arithmetic, not rounded decimals.
• S196 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S195 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S194 · premise_and_result_audit — Recompute Exp convolution coefficient term7 with exact rational arithmetic, not rounded decimals.
• S193 · premise_and_result_audit — Recompute Exp convolution denominator7 with exact rational arithmetic, not rounded decimals.
• S192 · premise_and_result_audit — Recompute Exp convolution right7 factorial step12 with exact rational arithmetic, not rounded decimals.
• S191 · premise_and_result_audit — Recompute Exp convolution right7 factorial step11 with exact rational arithmetic, not rounded decimals.
• S190 · premise_and_result_audit — Recompute Exp convolution right7 factorial step10 with exact rational arithmetic, not rounded decimals.
• S189 · premise_and_result_audit — Recompute Exp convolution right7 factorial step9 with exact rational arithmetic, not rounded decimals.
• S188 · premise_and_result_audit — Recompute Exp convolution right7 factorial step8 with exact rational arithmetic, not rounded decimals.
• S187 · premise_and_result_audit — Recompute Exp convolution right7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S186 · premise_and_result_audit — Recompute Exp convolution right7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S185 · premise_and_result_audit — Recompute Exp convolution right7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S184 · premise_and_result_audit — Recompute Exp convolution right7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S183 · premise_and_result_audit — Recompute Exp convolution right7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S182 · premise_and_result_audit — Recompute Exp convolution right7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Recompute Exp convolution right7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S180 · premise_and_result_audit — Recompute Exp convolution left7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Recompute Exp convolution left7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S178 · premise_and_result_audit — Recompute Exp convolution left7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Recompute Exp convolution left7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S176 · premise_and_result_audit — Recompute Exp convolution left7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S175 · premise_and_result_audit — Recompute Exp convolution left7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S174 · premise_and_result_audit — Recompute Exp convolution left7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S173 · premise_and_result_audit — Recompute Exp convolution numerator7 with exact rational arithmetic, not rounded decimals.
• S172 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S171 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S170 · premise_and_result_audit — Recompute Exp convolution coefficient term6 with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Recompute Exp convolution denominator6 with exact rational arithmetic, not rounded decimals.
• S168 · premise_and_result_audit — Recompute Exp convolution right6 factorial step13 with exact rational arithmetic, not rounded decimals.
• S167 · premise_and_result_audit — Recompute Exp convolution right6 factorial step12 with exact rational arithmetic, not rounded decimals.
• S166 · premise_and_result_audit — Recompute Exp convolution right6 factorial step11 with exact rational arithmetic, not rounded decimals.
• S165 · premise_and_result_audit — Recompute Exp convolution right6 factorial step10 with exact rational arithmetic, not rounded decimals.
• S164 · premise_and_result_audit — Recompute Exp convolution right6 factorial step9 with exact rational arithmetic, not rounded decimals.
• S163 · premise_and_result_audit — Recompute Exp convolution right6 factorial step8 with exact rational arithmetic, not rounded decimals.
• S162 · premise_and_result_audit — Recompute Exp convolution right6 factorial step7 with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Recompute Exp convolution right6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S160 · premise_and_result_audit — Recompute Exp convolution right6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Recompute Exp convolution right6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S158 · premise_and_result_audit — Recompute Exp convolution right6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Recompute Exp convolution right6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S156 · premise_and_result_audit — Recompute Exp convolution right6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S155 · premise_and_result_audit — Recompute Exp convolution left6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S154 · premise_and_result_audit — Recompute Exp convolution left6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S153 · premise_and_result_audit — Recompute Exp convolution left6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S152 · premise_and_result_audit — Recompute Exp convolution left6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Recompute Exp convolution left6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S150 · premise_and_result_audit — Recompute Exp convolution left6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S149 · premise_and_result_audit — Recompute Exp convolution numerator6 with exact rational arithmetic, not rounded decimals.
• S148 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S147 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S146 · premise_and_result_audit — Recompute Exp convolution coefficient term5 with exact rational arithmetic, not rounded decimals.
• S145 · premise_and_result_audit — Recompute Exp convolution denominator5 with exact rational arithmetic, not rounded decimals.
• S144 · premise_and_result_audit — Recompute Exp convolution right5 factorial step14 with exact rational arithmetic, not rounded decimals.
• S143 · premise_and_result_audit — Recompute Exp convolution right5 factorial step13 with exact rational arithmetic, not rounded decimals.
• S142 · premise_and_result_audit — Recompute Exp convolution right5 factorial step12 with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Recompute Exp convolution right5 factorial step11 with exact rational arithmetic, not rounded decimals.
• S140 · premise_and_result_audit — Recompute Exp convolution right5 factorial step10 with exact rational arithmetic, not rounded decimals.
• S139 · premise_and_result_audit — Recompute Exp convolution right5 factorial step9 with exact rational arithmetic, not rounded decimals.
• S138 · premise_and_result_audit — Recompute Exp convolution right5 factorial step8 with exact rational arithmetic, not rounded decimals.
• S137 · premise_and_result_audit — Recompute Exp convolution right5 factorial step7 with exact rational arithmetic, not rounded decimals.
• S136 · premise_and_result_audit — Recompute Exp convolution right5 factorial step6 with exact rational arithmetic, not rounded decimals.
• S135 · premise_and_result_audit — Recompute Exp convolution right5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S134 · premise_and_result_audit — Recompute Exp convolution right5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Recompute Exp convolution right5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S132 · premise_and_result_audit — Recompute Exp convolution right5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Recompute Exp convolution right5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S130 · premise_and_result_audit — Recompute Exp convolution left5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S129 · premise_and_result_audit — Recompute Exp convolution left5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S128 · premise_and_result_audit — Recompute Exp convolution left5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Recompute Exp convolution left5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S126 · premise_and_result_audit — Recompute Exp convolution left5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S125 · premise_and_result_audit — Recompute Exp convolution numerator5 with exact rational arithmetic, not rounded decimals.
• S124 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S123 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S122 · premise_and_result_audit — Recompute Exp convolution coefficient term4 with exact rational arithmetic, not rounded decimals.
• S121 · premise_and_result_audit — Recompute Exp convolution denominator4 with exact rational arithmetic, not rounded decimals.
• S120 · premise_and_result_audit — Recompute Exp convolution right4 factorial step15 with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Recompute Exp convolution right4 factorial step14 with exact rational arithmetic, not rounded decimals.
• S118 · premise_and_result_audit — Recompute Exp convolution right4 factorial step13 with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Recompute Exp convolution right4 factorial step12 with exact rational arithmetic, not rounded decimals.
• S116 · premise_and_result_audit — Recompute Exp convolution right4 factorial step11 with exact rational arithmetic, not rounded decimals.
• S115 · premise_and_result_audit — Recompute Exp convolution right4 factorial step10 with exact rational arithmetic, not rounded decimals.
• S114 · premise_and_result_audit — Recompute Exp convolution right4 factorial step9 with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Recompute Exp convolution right4 factorial step8 with exact rational arithmetic, not rounded decimals.
• S112 · premise_and_result_audit — Recompute Exp convolution right4 factorial step7 with exact rational arithmetic, not rounded decimals.
• S111 · premise_and_result_audit — Recompute Exp convolution right4 factorial step6 with exact rational arithmetic, not rounded decimals.
• S110 · premise_and_result_audit — Recompute Exp convolution right4 factorial step5 with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Recompute Exp convolution right4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S108 · premise_and_result_audit — Recompute Exp convolution right4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S107 · premise_and_result_audit — Recompute Exp convolution right4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S106 · premise_and_result_audit — Recompute Exp convolution right4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S105 · premise_and_result_audit — Recompute Exp convolution left4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S104 · premise_and_result_audit — Recompute Exp convolution left4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S103 · premise_and_result_audit — Recompute Exp convolution left4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S102 · premise_and_result_audit — Recompute Exp convolution left4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S101 · premise_and_result_audit — Recompute Exp convolution numerator4 with exact rational arithmetic, not rounded decimals.
• S100 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S099 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S098 · premise_and_result_audit — Recompute Exp convolution coefficient term3 with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Recompute Exp convolution denominator3 with exact rational arithmetic, not rounded decimals.
• S096 · premise_and_result_audit — Recompute Exp convolution right3 factorial step16 with exact rational arithmetic, not rounded decimals.
• S095 · premise_and_result_audit — Recompute Exp convolution right3 factorial step15 with exact rational arithmetic, not rounded decimals.
• S094 · premise_and_result_audit — Recompute Exp convolution right3 factorial step14 with exact rational arithmetic, not rounded decimals.
• S093 · premise_and_result_audit — Recompute Exp convolution right3 factorial step13 with exact rational arithmetic, not rounded decimals.
• S092 · premise_and_result_audit — Recompute Exp convolution right3 factorial step12 with exact rational arithmetic, not rounded decimals.
• S091 · premise_and_result_audit — Recompute Exp convolution right3 factorial step11 with exact rational arithmetic, not rounded decimals.
• S090 · premise_and_result_audit — Recompute Exp convolution right3 factorial step10 with exact rational arithmetic, not rounded decimals.
• S089 · premise_and_result_audit — Recompute Exp convolution right3 factorial step9 with exact rational arithmetic, not rounded decimals.
• S088 · premise_and_result_audit — Recompute Exp convolution right3 factorial step8 with exact rational arithmetic, not rounded decimals.
• S087 · premise_and_result_audit — Recompute Exp convolution right3 factorial step7 with exact rational arithmetic, not rounded decimals.
• S086 · premise_and_result_audit — Recompute Exp convolution right3 factorial step6 with exact rational arithmetic, not rounded decimals.
• S085 · premise_and_result_audit — Recompute Exp convolution right3 factorial step5 with exact rational arithmetic, not rounded decimals.
• S084 · premise_and_result_audit — Recompute Exp convolution right3 factorial step4 with exact rational arithmetic, not rounded decimals.
• S083 · premise_and_result_audit — Recompute Exp convolution right3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S082 · premise_and_result_audit — Recompute Exp convolution right3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S081 · premise_and_result_audit — Recompute Exp convolution right3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S080 · premise_and_result_audit — Recompute Exp convolution left3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S079 · premise_and_result_audit — Recompute Exp convolution left3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S078 · premise_and_result_audit — Recompute Exp convolution left3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S077 · premise_and_result_audit — Recompute Exp convolution numerator3 with exact rational arithmetic, not rounded decimals.
• S076 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S075 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S074 · premise_and_result_audit — Recompute Exp convolution coefficient term2 with exact rational arithmetic, not rounded decimals.
• S073 · premise_and_result_audit — Recompute Exp convolution denominator2 with exact rational arithmetic, not rounded decimals.
• S072 · premise_and_result_audit — Recompute Exp convolution right2 factorial step17 with exact rational arithmetic, not rounded decimals.
• S071 · premise_and_result_audit — Recompute Exp convolution right2 factorial step16 with exact rational arithmetic, not rounded decimals.
• S070 · premise_and_result_audit — Recompute Exp convolution right2 factorial step15 with exact rational arithmetic, not rounded decimals.
• S069 · premise_and_result_audit — Recompute Exp convolution right2 factorial step14 with exact rational arithmetic, not rounded decimals.
• S068 · premise_and_result_audit — Recompute Exp convolution right2 factorial step13 with exact rational arithmetic, not rounded decimals.
• S067 · premise_and_result_audit — Recompute Exp convolution right2 factorial step12 with exact rational arithmetic, not rounded decimals.
• S066 · premise_and_result_audit — Recompute Exp convolution right2 factorial step11 with exact rational arithmetic, not rounded decimals.
• S065 · premise_and_result_audit — Recompute Exp convolution right2 factorial step10 with exact rational arithmetic, not rounded decimals.
• S064 · premise_and_result_audit — Recompute Exp convolution right2 factorial step9 with exact rational arithmetic, not rounded decimals.
• S063 · premise_and_result_audit — Recompute Exp convolution right2 factorial step8 with exact rational arithmetic, not rounded decimals.
• S062 · premise_and_result_audit — Recompute Exp convolution right2 factorial step7 with exact rational arithmetic, not rounded decimals.
• S061 · premise_and_result_audit — Recompute Exp convolution right2 factorial step6 with exact rational arithmetic, not rounded decimals.
• S060 · premise_and_result_audit — Recompute Exp convolution right2 factorial step5 with exact rational arithmetic, not rounded decimals.
• S059 · premise_and_result_audit — Recompute Exp convolution right2 factorial step4 with exact rational arithmetic, not rounded decimals.
• S058 · premise_and_result_audit — Recompute Exp convolution right2 factorial step3 with exact rational arithmetic, not rounded decimals.
• S057 · premise_and_result_audit — Recompute Exp convolution right2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S056 · premise_and_result_audit — Recompute Exp convolution right2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S055 · premise_and_result_audit — Recompute Exp convolution left2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S054 · premise_and_result_audit — Recompute Exp convolution left2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S053 · premise_and_result_audit — Recompute Exp convolution numerator2 with exact rational arithmetic, not rounded decimals.
• S052 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S051 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S050 · premise_and_result_audit — Recompute Exp convolution coefficient term1 with exact rational arithmetic, not rounded decimals.
• S049 · premise_and_result_audit — Recompute Exp convolution denominator1 with exact rational arithmetic, not rounded decimals.
• S048 · premise_and_result_audit — Recompute Exp convolution right1 factorial step18 with exact rational arithmetic, not rounded decimals.
• S047 · premise_and_result_audit — Recompute Exp convolution right1 factorial step17 with exact rational arithmetic, not rounded decimals.
• S046 · premise_and_result_audit — Recompute Exp convolution right1 factorial step16 with exact rational arithmetic, not rounded decimals.
• S045 · premise_and_result_audit — Recompute Exp convolution right1 factorial step15 with exact rational arithmetic, not rounded decimals.
• S044 · premise_and_result_audit — Recompute Exp convolution right1 factorial step14 with exact rational arithmetic, not rounded decimals.
• S043 · premise_and_result_audit — Recompute Exp convolution right1 factorial step13 with exact rational arithmetic, not rounded decimals.
• S042 · premise_and_result_audit — Recompute Exp convolution right1 factorial step12 with exact rational arithmetic, not rounded decimals.
• S041 · premise_and_result_audit — Recompute Exp convolution right1 factorial step11 with exact rational arithmetic, not rounded decimals.
• S040 · premise_and_result_audit — Recompute Exp convolution right1 factorial step10 with exact rational arithmetic, not rounded decimals.
• S039 · premise_and_result_audit — Recompute Exp convolution right1 factorial step9 with exact rational arithmetic, not rounded decimals.
• S038 · premise_and_result_audit — Recompute Exp convolution right1 factorial step8 with exact rational arithmetic, not rounded decimals.
• S037 · premise_and_result_audit — Recompute Exp convolution right1 factorial step7 with exact rational arithmetic, not rounded decimals.
• S036 · premise_and_result_audit — Recompute Exp convolution right1 factorial step6 with exact rational arithmetic, not rounded decimals.
• S035 · premise_and_result_audit — Recompute Exp convolution right1 factorial step5 with exact rational arithmetic, not rounded decimals.
• S034 · premise_and_result_audit — Recompute Exp convolution right1 factorial step4 with exact rational arithmetic, not rounded decimals.
• S033 · premise_and_result_audit — Recompute Exp convolution right1 factorial step3 with exact rational arithmetic, not rounded decimals.
• S032 · premise_and_result_audit — Recompute Exp convolution right1 factorial step2 with exact rational arithmetic, not rounded decimals.
• S031 · premise_and_result_audit — Recompute Exp convolution right1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S030 · premise_and_result_audit — Recompute Exp convolution left1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S029 · premise_and_result_audit — Recompute Exp convolution numerator1 with exact rational arithmetic, not rounded decimals.
• S028 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S027 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S026 · premise_and_result_audit — Recompute Exp convolution coefficient term0 with exact rational arithmetic, not rounded decimals.
• S025 · premise_and_result_audit — Recompute Exp convolution denominator0 with exact rational arithmetic, not rounded decimals.
• S024 · premise_and_result_audit — Recompute Exp convolution right0 factorial step19 with exact rational arithmetic, not rounded decimals.
• S023 · premise_and_result_audit — Recompute Exp convolution right0 factorial step18 with exact rational arithmetic, not rounded decimals.
• S022 · premise_and_result_audit — Recompute Exp convolution right0 factorial step17 with exact rational arithmetic, not rounded decimals.
• S021 · premise_and_result_audit — Recompute Exp convolution right0 factorial step16 with exact rational arithmetic, not rounded decimals.
• S020 · premise_and_result_audit — Recompute Exp convolution right0 factorial step15 with exact rational arithmetic, not rounded decimals.
• S019 · premise_and_result_audit — Recompute Exp convolution right0 factorial step14 with exact rational arithmetic, not rounded decimals.
• S018 · premise_and_result_audit — Recompute Exp convolution right0 factorial step13 with exact rational arithmetic, not rounded decimals.
• S017 · premise_and_result_audit — Recompute Exp convolution right0 factorial step12 with exact rational arithmetic, not rounded decimals.
• S016 · premise_and_result_audit — Recompute Exp convolution right0 factorial step11 with exact rational arithmetic, not rounded decimals.
• S015 · premise_and_result_audit — Recompute Exp convolution right0 factorial step10 with exact rational arithmetic, not rounded decimals.
• S014 · premise_and_result_audit — Recompute Exp convolution right0 factorial step9 with exact rational arithmetic, not rounded decimals.
• S013 · premise_and_result_audit — Recompute Exp convolution right0 factorial step8 with exact rational arithmetic, not rounded decimals.
• S012 · premise_and_result_audit — Recompute Exp convolution right0 factorial step7 with exact rational arithmetic, not rounded decimals.
• S011 · premise_and_result_audit — Recompute Exp convolution right0 factorial step6 with exact rational arithmetic, not rounded decimals.
• S010 · premise_and_result_audit — Recompute Exp convolution right0 factorial step5 with exact rational arithmetic, not rounded decimals.
• S009 · premise_and_result_audit — Recompute Exp convolution right0 factorial step4 with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute Exp convolution right0 factorial step3 with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute Exp convolution right0 factorial step2 with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute Exp convolution right0 factorial step1 with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Recompute Exp convolution numerator0 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(20/21, -21/22, 19, [[0, -41209797661291758429/12132755312575326542353091425992704000], [1, 93446253200208069/1451286520642981643822140122726400], [2, -1907066391840981/3298378456006776463232136642560], [3, 1441471195647/440959686631921987063119872], [4, -16343210835/1252726382477051099611136], [5, 555891525/14235527073602853404672], [6, -14706125/161767353109123334144], [7, 214375/1272645260473872384], [8, -21875/86771267759582208], [9, 15625/50825732251738752], [10, -78125/254706226397918064], [11, 390625/1560075636687248142], [12, -15625000/93817275788055876903], [13, 625000000/6985122624583433016687], [14, -25000000000/653426470972395688560993], [15, 1000000000000/78589383736043590542381249], [16, -10000000000000/3150719838872293039017284619], [17, 400000000000000/715786261576532754954926751171], [18, -16000000000000000/258268697472478045856009479581609], [19, 640000000000000000/196730310556535776929773039037663801]], -1/51676388762462995371436759840422682365878499503552553575761575936000, -1/51676388762462995371436759840422682365878499503552553575761575936000, Yes, binomial_convolution_matches_the_declared_degree;the_general_addition_law_requires_all_degrees_plus_absolute_convergence_for_Cauchy_product_rearrangement)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.