Question 24213: 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=13/14, y=-14/15, declared degree=12. 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=13/14, y=-14/15, declared degree=12. 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]]

(13/14)^0

Exp convolution x power0 = 1

(-14/15)^12

Exp convolution y power12 = 56693912375296/129746337890625

Exp convolution numerator0 := mul(1, 56693912375296/129746337890625)

Exp convolution numerator0 = 56693912375296/129746337890625

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 denominator0 := mul(1, 479001600)

Exp convolution denominator0 = 479001600

Exp convolution coefficient term0 := div(56693912375296/129746337890625, 479001600)

Exp convolution coefficient term0 = 7909306972/8670299029541015625

(13/14)^1

Exp convolution x power1 = 13/14

(-14/15)^11

Exp convolution y power11 = -4049565169664/8649755859375

Exp convolution numerator1 := mul(13/14, -4049565169664/8649755859375)

Exp convolution numerator1 = -3760310514688/8649755859375

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 denominator1 := mul(1, 39916800)

Exp convolution denominator1 = 39916800

Exp convolution coefficient term1 := div(-3760310514688/8649755859375, 39916800)

Exp convolution coefficient term1 = -2098387564/192673311767578125

(13/14)^2

Exp convolution x power2 = 169/196

(-14/15)^10

Exp convolution y power10 = 289254654976/576650390625

Exp convolution numerator2 := mul(169/196, 289254654976/576650390625)

Exp convolution numerator2 = 249408350464/576650390625

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 denominator2 := mul(2, 3628800)

Exp convolution denominator2 = 7257600

Exp convolution coefficient term2 := div(249408350464/576650390625, 7257600)

Exp convolution coefficient term2 = 139178767/2335434082031250

(13/14)^3

Exp convolution x power3 = 2197/2744

(-14/15)^9

Exp convolution y power9 = -20661046784/38443359375

Exp convolution numerator3 := mul(2197/2744, -20661046784/38443359375)

Exp convolution numerator3 = -16542390592/38443359375

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 denominator3 := mul(6, 362880)

Exp convolution denominator3 = 2177280

Exp convolution coefficient term3 := div(-16542390592/38443359375, 2177280)

Exp convolution coefficient term3 = -36924979/186834726562500

(13/14)^4

Exp convolution x power4 = 28561/38416

(-14/15)^8

Exp convolution y power8 = 1475789056/2562890625

Exp convolution numerator4 := mul(28561/38416, 1475789056/2562890625)

Exp convolution numerator4 = 1097199376/2562890625

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 denominator4 := mul(24, 40320)

Exp convolution denominator4 = 967680

Exp convolution coefficient term4 := div(1097199376/2562890625, 967680)

Exp convolution coefficient term4 = 9796423/22143375000000

(13/14)^5

Exp convolution x power5 = 371293/537824

(-14/15)^7

Exp convolution y power7 = -105413504/170859375

Exp convolution numerator5 := mul(371293/537824, -105413504/170859375)

Exp convolution numerator5 = -72773428/170859375

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 denominator5 := mul(120, 5040)

Exp convolution denominator5 = 604800

Exp convolution coefficient term5 := div(-72773428/170859375, 604800)

Exp convolution coefficient term5 = -2599051/3690562500000

(13/14)^6

Exp convolution x power6 = 4826809/7529536

(-14/15)^6

Exp convolution y power6 = 7529536/11390625

Exp convolution numerator6 := mul(4826809/7529536, 7529536/11390625)

Exp convolution numerator6 = 4826809/11390625

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 denominator6 := mul(720, 720)

Exp convolution denominator6 = 518400

Exp convolution coefficient term6 := div(4826809/11390625, 518400)

Exp convolution coefficient term6 = 4826809/5904900000000

(13/14)^7

Exp convolution x power7 = 62748517/105413504

(-14/15)^5

Exp convolution y power5 = -537824/759375

Exp convolution numerator7 := mul(62748517/105413504, -537824/759375)

Exp convolution numerator7 = -62748517/148837500

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 denominator7 := mul(5040, 120)

Exp convolution denominator7 = 604800

Exp convolution coefficient term7 := div(-62748517/148837500, 604800)

Exp convolution coefficient term7 = -62748517/90016920000000

(13/14)^8

Exp convolution x power8 = 815730721/1475789056

(-14/15)^4

Exp convolution y power4 = 38416/50625

Exp convolution numerator8 := mul(815730721/1475789056, 38416/50625)

Exp convolution numerator8 = 815730721/1944810000

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 denominator8 := mul(40320, 24)

Exp convolution denominator8 = 967680

Exp convolution coefficient term8 := div(815730721/1944810000, 967680)

Exp convolution coefficient term8 = 815730721/1881953740800000

(13/14)^9

Exp convolution x power9 = 10604499373/20661046784

(-14/15)^3

Exp convolution y power3 = -2744/3375

Exp convolution numerator9 := mul(10604499373/20661046784, -2744/3375)

Exp convolution numerator9 = -10604499373/25412184000

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 denominator9 := mul(362880, 6)

Exp convolution denominator9 = 2177280

Exp convolution coefficient term9 := div(-10604499373/25412184000, 2177280)

Exp convolution coefficient term9 = -10604499373/55329439979520000

(13/14)^10

Exp convolution x power10 = 137858491849/289254654976

(-14/15)^2

Exp convolution y power2 = 196/225

Exp convolution numerator10 := mul(137858491849/289254654976, 196/225)

Exp convolution numerator10 = 137858491849/332052537600

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 denominator10 := mul(3628800, 2)

Exp convolution denominator10 = 7257600

Exp convolution coefficient term10 := div(137858491849/332052537600, 7257600)

Exp convolution coefficient term10 = 137858491849/2409904496885760000

(13/14)^11

Exp convolution x power11 = 1792160394037/4049565169664

(-14/15)^1

Exp convolution y power1 = -14/15

Exp convolution numerator11 := mul(1792160394037/4049565169664, -14/15)

Exp convolution numerator11 = -1792160394037/4338819824640

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 denominator11 := mul(39916800, 1)

Exp convolution denominator11 = 39916800

Exp convolution coefficient term11 := div(-1792160394037/4338819824640, 39916800)

Exp convolution coefficient term11 = -1792160394037/173191803176189952000

(13/14)^12

Exp convolution x power12 = 23298085122481/56693912375296

(-14/15)^0

Exp convolution y power0 = 1

Exp convolution numerator12 := mul(23298085122481/56693912375296, 1)

Exp convolution numerator12 = 23298085122481/56693912375296

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

source roles = [0]

derived = [1]

Exp convolution denominator12 := mul(479001600, 1)

Exp convolution denominator12 = 479001600

Exp convolution coefficient term12 := div(23298085122481/56693912375296, 479001600)

Exp convolution coefficient term12 = 23298085122481/27156474738026584473600

Exp complete declared-degree convolution := sum(7909306972/8670299029541015625, -2098387564/192673311767578125, 139178767/2335434082031250, -36924979/186834726562500, 9796423/22143375000000, -2599051/3690562500000, 4826809/5904900000000, -62748517/90016920000000, 815730721/1881953740800000, -10604499373/55329439979520000, 137858491849/2409904496885760000, -1792160394037/173191803176189952000, 23298085122481/27156474738026584473600)

Exp complete declared-degree convolution = 1/3523453147278219257625600000000000000

Exp ORIGINAL arguments sum := sum(13/14, -14/15)

Exp ORIGINAL arguments sum = -1/210

(-1/210)^12

Exp sum argument declared power = 1/7355827511386641000000000000

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 coefficient := div(1/7355827511386641000000000000, 479001600)

Exp sum argument coefficient = 1/3523453147278219257625600000000000000

source roles = [[13/14, -14/15], 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 = [[13/14, -14/15, 12], 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

• S242 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S241 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S240 · premise_and_result_audit — Recompute Exp sum argument coefficient with exact rational arithmetic, not rounded decimals.
• S239 · premise_and_result_audit — Recompute Exp sum argument factorial step12 with exact rational arithmetic, not rounded decimals.
• S238 · premise_and_result_audit — Recompute Exp sum argument factorial step11 with exact rational arithmetic, not rounded decimals.
• S237 · premise_and_result_audit — Recompute Exp sum argument factorial step10 with exact rational arithmetic, not rounded decimals.
• S236 · premise_and_result_audit — Recompute Exp sum argument factorial step9 with exact rational arithmetic, not rounded decimals.
• S235 · premise_and_result_audit — Recompute Exp sum argument factorial step8 with exact rational arithmetic, not rounded decimals.
• S234 · premise_and_result_audit — Recompute Exp sum argument factorial step7 with exact rational arithmetic, not rounded decimals.
• S233 · premise_and_result_audit — Recompute Exp sum argument factorial step6 with exact rational arithmetic, not rounded decimals.
• S232 · premise_and_result_audit — Recompute Exp sum argument factorial step5 with exact rational arithmetic, not rounded decimals.
• S231 · premise_and_result_audit — Recompute Exp sum argument factorial step4 with exact rational arithmetic, not rounded decimals.
• S230 · premise_and_result_audit — Recompute Exp sum argument factorial step3 with exact rational arithmetic, not rounded decimals.
• S229 · premise_and_result_audit — Recompute Exp sum argument factorial step2 with exact rational arithmetic, not rounded decimals.
• S228 · premise_and_result_audit — Recompute Exp sum argument factorial step1 with exact rational arithmetic, not rounded decimals.
• S227 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S226 · premise_and_result_audit — Recompute Exp ORIGINAL arguments sum with exact rational arithmetic, not rounded decimals.
• S225 · premise_and_result_audit — Recompute Exp complete declared-degree convolution with exact rational arithmetic, not rounded decimals.
• S224 · premise_and_result_audit — Recompute Exp convolution coefficient term12 with exact rational arithmetic, not rounded decimals.
• S223 · premise_and_result_audit — Recompute Exp convolution denominator12 with exact rational arithmetic, not rounded decimals.
• S222 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S221 · premise_and_result_audit — Recompute Exp convolution left12 factorial step12 with exact rational arithmetic, not rounded decimals.
• S220 · premise_and_result_audit — Recompute Exp convolution left12 factorial step11 with exact rational arithmetic, not rounded decimals.
• S219 · premise_and_result_audit — Recompute Exp convolution left12 factorial step10 with exact rational arithmetic, not rounded decimals.
• S218 · premise_and_result_audit — Recompute Exp convolution left12 factorial step9 with exact rational arithmetic, not rounded decimals.
• S217 · premise_and_result_audit — Recompute Exp convolution left12 factorial step8 with exact rational arithmetic, not rounded decimals.
• S216 · premise_and_result_audit — Recompute Exp convolution left12 factorial step7 with exact rational arithmetic, not rounded decimals.
• S215 · premise_and_result_audit — Recompute Exp convolution left12 factorial step6 with exact rational arithmetic, not rounded decimals.
• S214 · premise_and_result_audit — Recompute Exp convolution left12 factorial step5 with exact rational arithmetic, not rounded decimals.
• S213 · premise_and_result_audit — Recompute Exp convolution left12 factorial step4 with exact rational arithmetic, not rounded decimals.
• S212 · premise_and_result_audit — Recompute Exp convolution left12 factorial step3 with exact rational arithmetic, not rounded decimals.
• S211 · premise_and_result_audit — Recompute Exp convolution left12 factorial step2 with exact rational arithmetic, not rounded decimals.
• S210 · premise_and_result_audit — Recompute Exp convolution left12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S209 · premise_and_result_audit — Recompute Exp convolution numerator12 with exact rational arithmetic, not rounded decimals.
• S208 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S207 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S206 · premise_and_result_audit — Recompute Exp convolution coefficient term11 with exact rational arithmetic, not rounded decimals.
• S205 · premise_and_result_audit — Recompute Exp convolution denominator11 with exact rational arithmetic, not rounded decimals.
• S204 · premise_and_result_audit — Recompute Exp convolution right11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S203 · premise_and_result_audit — Recompute Exp convolution left11 factorial step11 with exact rational arithmetic, not rounded decimals.
• S202 · premise_and_result_audit — Recompute Exp convolution left11 factorial step10 with exact rational arithmetic, not rounded decimals.
• S201 · premise_and_result_audit — Recompute Exp convolution left11 factorial step9 with exact rational arithmetic, not rounded decimals.
• S200 · premise_and_result_audit — Recompute Exp convolution left11 factorial step8 with exact rational arithmetic, not rounded decimals.
• S199 · premise_and_result_audit — Recompute Exp convolution left11 factorial step7 with exact rational arithmetic, not rounded decimals.
• S198 · premise_and_result_audit — Recompute Exp convolution left11 factorial step6 with exact rational arithmetic, not rounded decimals.
• S197 · premise_and_result_audit — Recompute Exp convolution left11 factorial step5 with exact rational arithmetic, not rounded decimals.
• S196 · premise_and_result_audit — Recompute Exp convolution left11 factorial step4 with exact rational arithmetic, not rounded decimals.
• S195 · premise_and_result_audit — Recompute Exp convolution left11 factorial step3 with exact rational arithmetic, not rounded decimals.
• S194 · premise_and_result_audit — Recompute Exp convolution left11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S193 · premise_and_result_audit — Recompute Exp convolution left11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S192 · premise_and_result_audit — Recompute Exp convolution numerator11 with exact rational arithmetic, not rounded decimals.
• S191 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S190 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S189 · premise_and_result_audit — Recompute Exp convolution coefficient term10 with exact rational arithmetic, not rounded decimals.
• S188 · premise_and_result_audit — Recompute Exp convolution denominator10 with exact rational arithmetic, not rounded decimals.
• S187 · premise_and_result_audit — Recompute Exp convolution right10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S186 · premise_and_result_audit — Recompute Exp convolution right10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S185 · premise_and_result_audit — Recompute Exp convolution left10 factorial step10 with exact rational arithmetic, not rounded decimals.
• S184 · premise_and_result_audit — Recompute Exp convolution left10 factorial step9 with exact rational arithmetic, not rounded decimals.
• S183 · premise_and_result_audit — Recompute Exp convolution left10 factorial step8 with exact rational arithmetic, not rounded decimals.
• S182 · premise_and_result_audit — Recompute Exp convolution left10 factorial step7 with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Recompute Exp convolution left10 factorial step6 with exact rational arithmetic, not rounded decimals.
• S180 · premise_and_result_audit — Recompute Exp convolution left10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Recompute Exp convolution left10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S178 · premise_and_result_audit — Recompute Exp convolution left10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Recompute Exp convolution left10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S176 · premise_and_result_audit — Recompute Exp convolution left10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S175 · premise_and_result_audit — Recompute Exp convolution numerator10 with exact rational arithmetic, not rounded decimals.
• S174 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S173 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S172 · premise_and_result_audit — Recompute Exp convolution coefficient term9 with exact rational arithmetic, not rounded decimals.
• S171 · premise_and_result_audit — Recompute Exp convolution denominator9 with exact rational arithmetic, not rounded decimals.
• S170 · premise_and_result_audit — Recompute Exp convolution right9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Recompute Exp convolution right9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S168 · premise_and_result_audit — Recompute Exp convolution right9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S167 · premise_and_result_audit — Recompute Exp convolution left9 factorial step9 with exact rational arithmetic, not rounded decimals.
• S166 · premise_and_result_audit — Recompute Exp convolution left9 factorial step8 with exact rational arithmetic, not rounded decimals.
• S165 · premise_and_result_audit — Recompute Exp convolution left9 factorial step7 with exact rational arithmetic, not rounded decimals.
• S164 · premise_and_result_audit — Recompute Exp convolution left9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S163 · premise_and_result_audit — Recompute Exp convolution left9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S162 · premise_and_result_audit — Recompute Exp convolution left9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Recompute Exp convolution left9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S160 · premise_and_result_audit — Recompute Exp convolution left9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Recompute Exp convolution left9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S158 · premise_and_result_audit — Recompute Exp convolution numerator9 with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S156 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S155 · premise_and_result_audit — Recompute Exp convolution coefficient term8 with exact rational arithmetic, not rounded decimals.
• S154 · premise_and_result_audit — Recompute Exp convolution denominator8 with exact rational arithmetic, not rounded decimals.
• S153 · premise_and_result_audit — Recompute Exp convolution right8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S152 · premise_and_result_audit — Recompute Exp convolution right8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Recompute Exp convolution right8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S150 · premise_and_result_audit — Recompute Exp convolution right8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S149 · premise_and_result_audit — Recompute Exp convolution left8 factorial step8 with exact rational arithmetic, not rounded decimals.
• S148 · premise_and_result_audit — Recompute Exp convolution left8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S147 · premise_and_result_audit — Recompute Exp convolution left8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S146 · premise_and_result_audit — Recompute Exp convolution left8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S145 · premise_and_result_audit — Recompute Exp convolution left8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S144 · premise_and_result_audit — Recompute Exp convolution left8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S143 · premise_and_result_audit — Recompute Exp convolution left8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S142 · premise_and_result_audit — Recompute Exp convolution left8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Recompute Exp convolution numerator8 with exact rational arithmetic, not rounded decimals.
• S140 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S139 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S138 · premise_and_result_audit — Recompute Exp convolution coefficient term7 with exact rational arithmetic, not rounded decimals.
• S137 · premise_and_result_audit — Recompute Exp convolution denominator7 with exact rational arithmetic, not rounded decimals.
• S136 · premise_and_result_audit — Recompute Exp convolution right7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S135 · premise_and_result_audit — Recompute Exp convolution right7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S134 · premise_and_result_audit — Recompute Exp convolution right7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Recompute Exp convolution right7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S132 · premise_and_result_audit — Recompute Exp convolution right7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Recompute Exp convolution left7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S130 · premise_and_result_audit — Recompute Exp convolution left7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S129 · premise_and_result_audit — Recompute Exp convolution left7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S128 · premise_and_result_audit — Recompute Exp convolution left7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Recompute Exp convolution left7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S126 · premise_and_result_audit — Recompute Exp convolution left7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S125 · premise_and_result_audit — Recompute Exp convolution left7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S124 · premise_and_result_audit — Recompute Exp convolution numerator7 with exact rational arithmetic, not rounded decimals.
• 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 — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S121 · premise_and_result_audit — Recompute Exp convolution coefficient term6 with exact rational arithmetic, not rounded decimals.
• S120 · premise_and_result_audit — Recompute Exp convolution denominator6 with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Recompute Exp convolution right6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S118 · premise_and_result_audit — Recompute Exp convolution right6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Recompute Exp convolution right6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S116 · premise_and_result_audit — Recompute Exp convolution right6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S115 · premise_and_result_audit — Recompute Exp convolution right6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S114 · premise_and_result_audit — Recompute Exp convolution right6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Recompute Exp convolution left6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S112 · premise_and_result_audit — Recompute Exp convolution left6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S111 · premise_and_result_audit — Recompute Exp convolution left6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S110 · premise_and_result_audit — Recompute Exp convolution left6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Recompute Exp convolution left6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S108 · premise_and_result_audit — Recompute Exp convolution left6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S107 · premise_and_result_audit — Recompute Exp convolution numerator6 with exact rational arithmetic, not rounded decimals.
• S106 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S105 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S104 · premise_and_result_audit — Recompute Exp convolution coefficient term5 with exact rational arithmetic, not rounded decimals.
• S103 · premise_and_result_audit — Recompute Exp convolution denominator5 with exact rational arithmetic, not rounded decimals.
• S102 · premise_and_result_audit — Recompute Exp convolution right5 factorial step7 with exact rational arithmetic, not rounded decimals.
• S101 · premise_and_result_audit — Recompute Exp convolution right5 factorial step6 with exact rational arithmetic, not rounded decimals.
• S100 · premise_and_result_audit — Recompute Exp convolution right5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S099 · premise_and_result_audit — Recompute Exp convolution right5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S098 · premise_and_result_audit — Recompute Exp convolution right5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Recompute Exp convolution right5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S096 · premise_and_result_audit — Recompute Exp convolution right5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S095 · premise_and_result_audit — Recompute Exp convolution left5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S094 · premise_and_result_audit — Recompute Exp convolution left5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S093 · premise_and_result_audit — Recompute Exp convolution left5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S092 · premise_and_result_audit — Recompute Exp convolution left5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S091 · premise_and_result_audit — Recompute Exp convolution left5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S090 · premise_and_result_audit — Recompute Exp convolution numerator5 with exact rational arithmetic, not rounded decimals.
• S089 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S088 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S087 · premise_and_result_audit — Recompute Exp convolution coefficient term4 with exact rational arithmetic, not rounded decimals.
• S086 · premise_and_result_audit — Recompute Exp convolution denominator4 with exact rational arithmetic, not rounded decimals.
• S085 · premise_and_result_audit — Recompute Exp convolution right4 factorial step8 with exact rational arithmetic, not rounded decimals.
• S084 · premise_and_result_audit — Recompute Exp convolution right4 factorial step7 with exact rational arithmetic, not rounded decimals.
• S083 · premise_and_result_audit — Recompute Exp convolution right4 factorial step6 with exact rational arithmetic, not rounded decimals.
• S082 · premise_and_result_audit — Recompute Exp convolution right4 factorial step5 with exact rational arithmetic, not rounded decimals.
• S081 · premise_and_result_audit — Recompute Exp convolution right4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S080 · premise_and_result_audit — Recompute Exp convolution right4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S079 · premise_and_result_audit — Recompute Exp convolution right4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S078 · premise_and_result_audit — Recompute Exp convolution right4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S077 · premise_and_result_audit — Recompute Exp convolution left4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S076 · premise_and_result_audit — Recompute Exp convolution left4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S075 · premise_and_result_audit — Recompute Exp convolution left4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S074 · premise_and_result_audit — Recompute Exp convolution left4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S073 · premise_and_result_audit — Recompute Exp convolution numerator4 with exact rational arithmetic, not rounded decimals.
• S072 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S071 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S070 · premise_and_result_audit — Recompute Exp convolution coefficient term3 with exact rational arithmetic, not rounded decimals.
• S069 · premise_and_result_audit — Recompute Exp convolution denominator3 with exact rational arithmetic, not rounded decimals.
• S068 · premise_and_result_audit — Recompute Exp convolution right3 factorial step9 with exact rational arithmetic, not rounded decimals.
• S067 · premise_and_result_audit — Recompute Exp convolution right3 factorial step8 with exact rational arithmetic, not rounded decimals.
• S066 · premise_and_result_audit — Recompute Exp convolution right3 factorial step7 with exact rational arithmetic, not rounded decimals.
• S065 · premise_and_result_audit — Recompute Exp convolution right3 factorial step6 with exact rational arithmetic, not rounded decimals.
• S064 · premise_and_result_audit — Recompute Exp convolution right3 factorial step5 with exact rational arithmetic, not rounded decimals.
• S063 · premise_and_result_audit — Recompute Exp convolution right3 factorial step4 with exact rational arithmetic, not rounded decimals.
• S062 · premise_and_result_audit — Recompute Exp convolution right3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S061 · premise_and_result_audit — Recompute Exp convolution right3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S060 · premise_and_result_audit — Recompute Exp convolution right3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S059 · premise_and_result_audit — Recompute Exp convolution left3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S058 · premise_and_result_audit — Recompute Exp convolution left3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S057 · premise_and_result_audit — Recompute Exp convolution left3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S056 · premise_and_result_audit — Recompute Exp convolution numerator3 with exact rational arithmetic, not rounded decimals.
• S055 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S054 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S053 · premise_and_result_audit — Recompute Exp convolution coefficient term2 with exact rational arithmetic, not rounded decimals.
• S052 · premise_and_result_audit — Recompute Exp convolution denominator2 with exact rational arithmetic, not rounded decimals.
• S051 · premise_and_result_audit — Recompute Exp convolution right2 factorial step10 with exact rational arithmetic, not rounded decimals.
• S050 · premise_and_result_audit — Recompute Exp convolution right2 factorial step9 with exact rational arithmetic, not rounded decimals.
• S049 · premise_and_result_audit — Recompute Exp convolution right2 factorial step8 with exact rational arithmetic, not rounded decimals.
• S048 · premise_and_result_audit — Recompute Exp convolution right2 factorial step7 with exact rational arithmetic, not rounded decimals.
• S047 · premise_and_result_audit — Recompute Exp convolution right2 factorial step6 with exact rational arithmetic, not rounded decimals.
• S046 · premise_and_result_audit — Recompute Exp convolution right2 factorial step5 with exact rational arithmetic, not rounded decimals.
• S045 · premise_and_result_audit — Recompute Exp convolution right2 factorial step4 with exact rational arithmetic, not rounded decimals.
• S044 · premise_and_result_audit — Recompute Exp convolution right2 factorial step3 with exact rational arithmetic, not rounded decimals.
• S043 · premise_and_result_audit — Recompute Exp convolution right2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S042 · premise_and_result_audit — Recompute Exp convolution right2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S041 · premise_and_result_audit — Recompute Exp convolution left2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S040 · premise_and_result_audit — Recompute Exp convolution left2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S039 · premise_and_result_audit — Recompute Exp convolution numerator2 with exact rational arithmetic, not rounded decimals.
• S038 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S037 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S036 · premise_and_result_audit — Recompute Exp convolution coefficient term1 with exact rational arithmetic, not rounded decimals.
• S035 · premise_and_result_audit — Recompute Exp convolution denominator1 with exact rational arithmetic, not rounded decimals.
• S034 · premise_and_result_audit — Recompute Exp convolution right1 factorial step11 with exact rational arithmetic, not rounded decimals.
• S033 · premise_and_result_audit — Recompute Exp convolution right1 factorial step10 with exact rational arithmetic, not rounded decimals.
• S032 · premise_and_result_audit — Recompute Exp convolution right1 factorial step9 with exact rational arithmetic, not rounded decimals.
• S031 · premise_and_result_audit — Recompute Exp convolution right1 factorial step8 with exact rational arithmetic, not rounded decimals.
• S030 · premise_and_result_audit — Recompute Exp convolution right1 factorial step7 with exact rational arithmetic, not rounded decimals.
• S029 · premise_and_result_audit — Recompute Exp convolution right1 factorial step6 with exact rational arithmetic, not rounded decimals.
• S028 · premise_and_result_audit — Recompute Exp convolution right1 factorial step5 with exact rational arithmetic, not rounded decimals.
• S027 · premise_and_result_audit — Recompute Exp convolution right1 factorial step4 with exact rational arithmetic, not rounded decimals.
• S026 · premise_and_result_audit — Recompute Exp convolution right1 factorial step3 with exact rational arithmetic, not rounded decimals.
• S025 · premise_and_result_audit — Recompute Exp convolution right1 factorial step2 with exact rational arithmetic, not rounded decimals.
• S024 · premise_and_result_audit — Recompute Exp convolution right1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S023 · premise_and_result_audit — Recompute Exp convolution left1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S022 · premise_and_result_audit — Recompute Exp convolution numerator1 with exact rational arithmetic, not rounded decimals.
• S021 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S020 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S019 · premise_and_result_audit — Recompute Exp convolution coefficient term0 with exact rational arithmetic, not rounded decimals.
• S018 · premise_and_result_audit — Recompute Exp convolution denominator0 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

(13/14, -14/15, 12, [[0, 7909306972/8670299029541015625], [1, -2098387564/192673311767578125], [2, 139178767/2335434082031250], [3, -36924979/186834726562500], [4, 9796423/22143375000000], [5, -2599051/3690562500000], [6, 4826809/5904900000000], [7, -62748517/90016920000000], [8, 815730721/1881953740800000], [9, -10604499373/55329439979520000], [10, 137858491849/2409904496885760000], [11, -1792160394037/173191803176189952000], [12, 23298085122481/27156474738026584473600]], 1/3523453147278219257625600000000000000, 1/3523453147278219257625600000000000000, 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.