Question 24214: 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=14/15, y=-15/16, declared degree=13. 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=14/15, y=-15/16, declared degree=13. 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]]

(14/15)^0

Exp convolution x power0 = 1

(-15/16)^13

Exp convolution y power13 = -1946195068359375/4503599627370496

Exp convolution numerator0 := mul(1, -1946195068359375/4503599627370496)

Exp convolution numerator0 = -1946195068359375/4503599627370496

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 denominator0 := mul(1, 6227020800)

Exp convolution denominator0 = 6227020800

Exp convolution coefficient term0 := div(-1946195068359375/4503599627370496, 6227020800)

Exp convolution coefficient term0 = -320361328125/4616297704445815291904

(14/15)^1

Exp convolution x power1 = 14/15

(-15/16)^12

Exp convolution y power12 = 129746337890625/281474976710656

Exp convolution numerator1 := mul(14/15, 129746337890625/281474976710656)

Exp convolution numerator1 = 60548291015625/140737488355328

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 denominator1 := mul(1, 479001600)

Exp convolution denominator1 = 479001600

Exp convolution coefficient term1 := div(60548291015625/140737488355328, 479001600)

Exp convolution coefficient term1 = 1423828125/1585267068834414592

(14/15)^2

Exp convolution x power2 = 196/225

(-15/16)^11

Exp convolution y power11 = -8649755859375/17592186044416

Exp convolution numerator2 := mul(196/225, -8649755859375/17592186044416)

Exp convolution numerator2 = -1883724609375/4398046511104

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 denominator2 := mul(2, 39916800)

Exp convolution denominator2 = 79833600

Exp convolution coefficient term2 := div(-1883724609375/4398046511104, 79833600)

Exp convolution coefficient term2 = -132890625/24769797950537728

(14/15)^3

Exp convolution x power3 = 2744/3375

(-15/16)^10

Exp convolution y power10 = 576650390625/1099511627776

Exp convolution numerator3 := mul(2744/3375, 576650390625/1099511627776)

Exp convolution numerator3 = 58604765625/137438953472

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 denominator3 := mul(6, 3628800)

Exp convolution denominator3 = 21772800

Exp convolution coefficient term3 := div(58604765625/137438953472, 21772800)

Exp convolution coefficient term3 = 1378125/70368744177664

(14/15)^4

Exp convolution x power4 = 38416/50625

(-15/16)^9

Exp convolution y power9 = -38443359375/68719476736

Exp convolution numerator4 := mul(38416/50625, -38443359375/68719476736)

Exp convolution numerator4 = -1823259375/4294967296

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 denominator4 := mul(24, 362880)

Exp convolution denominator4 = 8709120

Exp convolution coefficient term4 := div(-1823259375/4294967296, 8709120)

Exp convolution coefficient term4 = -214375/4398046511104

(14/15)^5

Exp convolution x power5 = 537824/759375

(-15/16)^8

Exp convolution y power8 = 2562890625/4294967296

Exp convolution numerator5 := mul(537824/759375, 2562890625/4294967296)

Exp convolution numerator5 = 56723625/134217728

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 denominator5 := mul(120, 40320)

Exp convolution denominator5 = 4838400

Exp convolution coefficient term5 := div(56723625/134217728, 4838400)

Exp convolution coefficient term5 = 12005/137438953472

(14/15)^6

Exp convolution x power6 = 7529536/11390625

(-15/16)^7

Exp convolution y power7 = -170859375/268435456

Exp convolution numerator6 := mul(7529536/11390625, -170859375/268435456)

Exp convolution numerator6 = -1764735/4194304

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 denominator6 := mul(720, 5040)

Exp convolution denominator6 = 3628800

Exp convolution coefficient term6 := div(-1764735/4194304, 3628800)

Exp convolution coefficient term6 = -16807/144955146240

(14/15)^7

Exp convolution x power7 = 105413504/170859375

(-15/16)^6

Exp convolution y power6 = 11390625/16777216

Exp convolution numerator7 := mul(105413504/170859375, 11390625/16777216)

Exp convolution numerator7 = 823543/1966080

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 denominator7 := mul(5040, 720)

Exp convolution denominator7 = 3628800

Exp convolution coefficient term7 := div(823543/1966080, 3628800)

Exp convolution coefficient term7 = 117649/1019215872000

(14/15)^8

Exp convolution x power8 = 1475789056/2562890625

(-15/16)^5

Exp convolution y power5 = -759375/1048576

Exp convolution numerator8 := mul(1475789056/2562890625, -759375/1048576)

Exp convolution numerator8 = -5764801/13824000

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 denominator8 := mul(40320, 120)

Exp convolution denominator8 = 4838400

Exp convolution coefficient term8 := div(-5764801/13824000, 4838400)

Exp convolution coefficient term8 = -823543/9555148800000

(14/15)^9

Exp convolution x power9 = 20661046784/38443359375

(-15/16)^4

Exp convolution y power4 = 50625/65536

Exp convolution numerator9 := mul(20661046784/38443359375, 50625/65536)

Exp convolution numerator9 = 40353607/97200000

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 denominator9 := mul(362880, 24)

Exp convolution denominator9 = 8709120

Exp convolution coefficient term9 := div(40353607/97200000, 8709120)

Exp convolution coefficient term9 = 5764801/120932352000000

(14/15)^10

Exp convolution x power10 = 289254654976/576650390625

(-15/16)^3

Exp convolution y power3 = -3375/4096

Exp convolution numerator10 := mul(289254654976/576650390625, -3375/4096)

Exp convolution numerator10 = -282475249/683437500

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 denominator10 := mul(3628800, 6)

Exp convolution denominator10 = 21772800

Exp convolution coefficient term10 := div(-282475249/683437500, 21772800)

Exp convolution coefficient term10 = -40353607/2125764000000000

(14/15)^11

Exp convolution x power11 = 4049565169664/8649755859375

(-15/16)^2

Exp convolution y power2 = 225/256

Exp convolution numerator11 := mul(4049565169664/8649755859375, 225/256)

Exp convolution numerator11 = 15818613944/38443359375

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 denominator11 := mul(39916800, 2)

Exp convolution denominator11 = 79833600

Exp convolution coefficient term11 := div(15818613944/38443359375, 79833600)

Exp convolution coefficient term11 = 282475249/54804853125000000

(14/15)^12

Exp convolution x power12 = 56693912375296/129746337890625

(-15/16)^1

Exp convolution y power1 = -15/16

Exp convolution numerator12 := mul(56693912375296/129746337890625, -15/16)

Exp convolution numerator12 = -3543369523456/8649755859375

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 denominator12 := mul(479001600, 1)

Exp convolution denominator12 = 479001600

Exp convolution coefficient term12 := div(-3543369523456/8649755859375, 479001600)

Exp convolution coefficient term12 = -1977326743/2312079741210937500

(14/15)^13

Exp convolution x power13 = 793714773254144/1946195068359375

(-15/16)^0

Exp convolution y power0 = 1

Exp convolution numerator13 := mul(793714773254144/1946195068359375, 1)

Exp convolution numerator13 = 793714773254144/1946195068359375

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

source roles = [0]

derived = [1]

Exp convolution denominator13 := mul(6227020800, 1)

Exp convolution denominator13 = 6227020800

Exp convolution coefficient term13 := div(793714773254144/1946195068359375, 6227020800)

Exp convolution coefficient term13 = 110730297608/1690708310760498046875

Exp complete declared-degree convolution := sum(-320361328125/4616297704445815291904, 1423828125/1585267068834414592, -132890625/24769797950537728, 1378125/70368744177664, -214375/4398046511104, 12005/137438953472, -16807/144955146240, 117649/1019215872000, -823543/9555148800000, 5764801/120932352000000, -40353607/2125764000000000, 282475249/54804853125000000, -1977326743/2312079741210937500, 110730297608/1690708310760498046875)

Exp complete declared-degree convolution = -1/54579111145812232494907392000000000000000

Exp ORIGINAL arguments sum := sum(14/15, -15/16)

Exp ORIGINAL arguments sum = -1/240

(-1/240)^13

Exp sum argument declared power = -1/8764883384653578240000000000000

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 coefficient := div(-1/8764883384653578240000000000000, 6227020800)

Exp sum argument coefficient = -1/54579111145812232494907392000000000000000

source roles = [[14/15, -15/16], 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 = [[14/15, -15/16, 13], 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

• S274 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S273 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S272 · premise_and_result_audit — Recompute Exp sum argument coefficient with exact rational arithmetic, not rounded decimals.
• S271 · premise_and_result_audit — Recompute Exp sum argument factorial step13 with exact rational arithmetic, not rounded decimals.
• S270 · premise_and_result_audit — Recompute Exp sum argument factorial step12 with exact rational arithmetic, not rounded decimals.
• S269 · premise_and_result_audit — Recompute Exp sum argument factorial step11 with exact rational arithmetic, not rounded decimals.
• S268 · premise_and_result_audit — Recompute Exp sum argument factorial step10 with exact rational arithmetic, not rounded decimals.
• S267 · premise_and_result_audit — Recompute Exp sum argument factorial step9 with exact rational arithmetic, not rounded decimals.
• S266 · premise_and_result_audit — Recompute Exp sum argument factorial step8 with exact rational arithmetic, not rounded decimals.
• S265 · premise_and_result_audit — Recompute Exp sum argument factorial step7 with exact rational arithmetic, not rounded decimals.
• S264 · premise_and_result_audit — Recompute Exp sum argument factorial step6 with exact rational arithmetic, not rounded decimals.
• S263 · premise_and_result_audit — Recompute Exp sum argument factorial step5 with exact rational arithmetic, not rounded decimals.
• S262 · premise_and_result_audit — Recompute Exp sum argument factorial step4 with exact rational arithmetic, not rounded decimals.
• S261 · premise_and_result_audit — Recompute Exp sum argument factorial step3 with exact rational arithmetic, not rounded decimals.
• S260 · premise_and_result_audit — Recompute Exp sum argument factorial step2 with exact rational arithmetic, not rounded decimals.
• S259 · premise_and_result_audit — Recompute Exp sum argument factorial step1 with exact rational arithmetic, not rounded decimals.
• S258 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S257 · premise_and_result_audit — Recompute Exp ORIGINAL arguments sum with exact rational arithmetic, not rounded decimals.
• S256 · premise_and_result_audit — Recompute Exp complete declared-degree convolution with exact rational arithmetic, not rounded decimals.
• S255 · premise_and_result_audit — Recompute Exp convolution coefficient term13 with exact rational arithmetic, not rounded decimals.
• S254 · premise_and_result_audit — Recompute Exp convolution denominator13 with exact rational arithmetic, not rounded decimals.
• S253 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S252 · premise_and_result_audit — Recompute Exp convolution left13 factorial step13 with exact rational arithmetic, not rounded decimals.
• S251 · premise_and_result_audit — Recompute Exp convolution left13 factorial step12 with exact rational arithmetic, not rounded decimals.
• S250 · premise_and_result_audit — Recompute Exp convolution left13 factorial step11 with exact rational arithmetic, not rounded decimals.
• S249 · premise_and_result_audit — Recompute Exp convolution left13 factorial step10 with exact rational arithmetic, not rounded decimals.
• S248 · premise_and_result_audit — Recompute Exp convolution left13 factorial step9 with exact rational arithmetic, not rounded decimals.
• S247 · premise_and_result_audit — Recompute Exp convolution left13 factorial step8 with exact rational arithmetic, not rounded decimals.
• S246 · premise_and_result_audit — Recompute Exp convolution left13 factorial step7 with exact rational arithmetic, not rounded decimals.
• S245 · premise_and_result_audit — Recompute Exp convolution left13 factorial step6 with exact rational arithmetic, not rounded decimals.
• S244 · premise_and_result_audit — Recompute Exp convolution left13 factorial step5 with exact rational arithmetic, not rounded decimals.
• S243 · premise_and_result_audit — Recompute Exp convolution left13 factorial step4 with exact rational arithmetic, not rounded decimals.
• S242 · premise_and_result_audit — Recompute Exp convolution left13 factorial step3 with exact rational arithmetic, not rounded decimals.
• S241 · premise_and_result_audit — Recompute Exp convolution left13 factorial step2 with exact rational arithmetic, not rounded decimals.
• S240 · premise_and_result_audit — Recompute Exp convolution left13 factorial step1 with exact rational arithmetic, not rounded decimals.
• S239 · premise_and_result_audit — Recompute Exp convolution numerator13 with exact rational arithmetic, not rounded decimals.
• S238 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S237 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S236 · premise_and_result_audit — Recompute Exp convolution coefficient term12 with exact rational arithmetic, not rounded decimals.
• S235 · premise_and_result_audit — Recompute Exp convolution denominator12 with exact rational arithmetic, not rounded decimals.
• S234 · premise_and_result_audit — Recompute Exp convolution right12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S233 · premise_and_result_audit — Recompute Exp convolution left12 factorial step12 with exact rational arithmetic, not rounded decimals.
• S232 · premise_and_result_audit — Recompute Exp convolution left12 factorial step11 with exact rational arithmetic, not rounded decimals.
• S231 · premise_and_result_audit — Recompute Exp convolution left12 factorial step10 with exact rational arithmetic, not rounded decimals.
• S230 · premise_and_result_audit — Recompute Exp convolution left12 factorial step9 with exact rational arithmetic, not rounded decimals.
• S229 · premise_and_result_audit — Recompute Exp convolution left12 factorial step8 with exact rational arithmetic, not rounded decimals.
• S228 · premise_and_result_audit — Recompute Exp convolution left12 factorial step7 with exact rational arithmetic, not rounded decimals.
• S227 · premise_and_result_audit — Recompute Exp convolution left12 factorial step6 with exact rational arithmetic, not rounded decimals.
• S226 · premise_and_result_audit — Recompute Exp convolution left12 factorial step5 with exact rational arithmetic, not rounded decimals.
• S225 · premise_and_result_audit — Recompute Exp convolution left12 factorial step4 with exact rational arithmetic, not rounded decimals.
• S224 · premise_and_result_audit — Recompute Exp convolution left12 factorial step3 with exact rational arithmetic, not rounded decimals.
• S223 · premise_and_result_audit — Recompute Exp convolution left12 factorial step2 with exact rational arithmetic, not rounded decimals.
• S222 · premise_and_result_audit — Recompute Exp convolution left12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S221 · premise_and_result_audit — Recompute Exp convolution numerator12 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 term11 with exact rational arithmetic, not rounded decimals.
• S217 · premise_and_result_audit — Recompute Exp convolution denominator11 with exact rational arithmetic, not rounded decimals.
• S216 · premise_and_result_audit — Recompute Exp convolution right11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S215 · premise_and_result_audit — Recompute Exp convolution right11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S214 · premise_and_result_audit — Recompute Exp convolution left11 factorial step11 with exact rational arithmetic, not rounded decimals.
• S213 · premise_and_result_audit — Recompute Exp convolution left11 factorial step10 with exact rational arithmetic, not rounded decimals.
• S212 · premise_and_result_audit — Recompute Exp convolution left11 factorial step9 with exact rational arithmetic, not rounded decimals.
• S211 · premise_and_result_audit — Recompute Exp convolution left11 factorial step8 with exact rational arithmetic, not rounded decimals.
• S210 · premise_and_result_audit — Recompute Exp convolution left11 factorial step7 with exact rational arithmetic, not rounded decimals.
• S209 · premise_and_result_audit — Recompute Exp convolution left11 factorial step6 with exact rational arithmetic, not rounded decimals.
• S208 · premise_and_result_audit — Recompute Exp convolution left11 factorial step5 with exact rational arithmetic, not rounded decimals.
• S207 · premise_and_result_audit — Recompute Exp convolution left11 factorial step4 with exact rational arithmetic, not rounded decimals.
• S206 · premise_and_result_audit — Recompute Exp convolution left11 factorial step3 with exact rational arithmetic, not rounded decimals.
• S205 · premise_and_result_audit — Recompute Exp convolution left11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S204 · premise_and_result_audit — Recompute Exp convolution left11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S203 · premise_and_result_audit — Recompute Exp convolution numerator11 with exact rational arithmetic, not rounded decimals.
• S202 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S201 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S200 · premise_and_result_audit — Recompute Exp convolution coefficient term10 with exact rational arithmetic, not rounded decimals.
• S199 · premise_and_result_audit — Recompute Exp convolution denominator10 with exact rational arithmetic, not rounded decimals.
• S198 · premise_and_result_audit — Recompute Exp convolution right10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S197 · premise_and_result_audit — Recompute Exp convolution right10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S196 · premise_and_result_audit — Recompute Exp convolution right10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S195 · premise_and_result_audit — Recompute Exp convolution left10 factorial step10 with exact rational arithmetic, not rounded decimals.
• S194 · premise_and_result_audit — Recompute Exp convolution left10 factorial step9 with exact rational arithmetic, not rounded decimals.
• S193 · premise_and_result_audit — Recompute Exp convolution left10 factorial step8 with exact rational arithmetic, not rounded decimals.
• S192 · premise_and_result_audit — Recompute Exp convolution left10 factorial step7 with exact rational arithmetic, not rounded decimals.
• S191 · premise_and_result_audit — Recompute Exp convolution left10 factorial step6 with exact rational arithmetic, not rounded decimals.
• S190 · premise_and_result_audit — Recompute Exp convolution left10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S189 · premise_and_result_audit — Recompute Exp convolution left10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S188 · premise_and_result_audit — Recompute Exp convolution left10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S187 · premise_and_result_audit — Recompute Exp convolution left10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S186 · premise_and_result_audit — Recompute Exp convolution left10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S185 · premise_and_result_audit — Recompute Exp convolution numerator10 with exact rational arithmetic, not rounded decimals.
• S184 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S183 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S182 · premise_and_result_audit — Recompute Exp convolution coefficient term9 with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Recompute Exp convolution denominator9 with exact rational arithmetic, not rounded decimals.
• S180 · premise_and_result_audit — Recompute Exp convolution right9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Recompute Exp convolution right9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S178 · premise_and_result_audit — Recompute Exp convolution right9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Recompute Exp convolution right9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S176 · premise_and_result_audit — Recompute Exp convolution left9 factorial step9 with exact rational arithmetic, not rounded decimals.
• S175 · premise_and_result_audit — Recompute Exp convolution left9 factorial step8 with exact rational arithmetic, not rounded decimals.
• S174 · premise_and_result_audit — Recompute Exp convolution left9 factorial step7 with exact rational arithmetic, not rounded decimals.
• S173 · premise_and_result_audit — Recompute Exp convolution left9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S172 · premise_and_result_audit — Recompute Exp convolution left9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S171 · premise_and_result_audit — Recompute Exp convolution left9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S170 · premise_and_result_audit — Recompute Exp convolution left9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Recompute Exp convolution left9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S168 · premise_and_result_audit — Recompute Exp convolution left9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S167 · premise_and_result_audit — Recompute Exp convolution numerator9 with exact rational arithmetic, not rounded decimals.
• S166 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S165 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S164 · premise_and_result_audit — Recompute Exp convolution coefficient term8 with exact rational arithmetic, not rounded decimals.
• S163 · premise_and_result_audit — Recompute Exp convolution denominator8 with exact rational arithmetic, not rounded decimals.
• S162 · premise_and_result_audit — Recompute Exp convolution right8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Recompute Exp convolution right8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S160 · premise_and_result_audit — Recompute Exp convolution right8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Recompute Exp convolution right8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S158 · premise_and_result_audit — Recompute Exp convolution right8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Recompute Exp convolution left8 factorial step8 with exact rational arithmetic, not rounded decimals.
• S156 · premise_and_result_audit — Recompute Exp convolution left8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S155 · premise_and_result_audit — Recompute Exp convolution left8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S154 · premise_and_result_audit — Recompute Exp convolution left8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S153 · premise_and_result_audit — Recompute Exp convolution left8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S152 · premise_and_result_audit — Recompute Exp convolution left8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Recompute Exp convolution left8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S150 · premise_and_result_audit — Recompute Exp convolution left8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S149 · premise_and_result_audit — Recompute Exp convolution numerator8 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 term7 with exact rational arithmetic, not rounded decimals.
• S145 · premise_and_result_audit — Recompute Exp convolution denominator7 with exact rational arithmetic, not rounded decimals.
• S144 · premise_and_result_audit — Recompute Exp convolution right7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S143 · premise_and_result_audit — Recompute Exp convolution right7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S142 · premise_and_result_audit — Recompute Exp convolution right7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Recompute Exp convolution right7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S140 · premise_and_result_audit — Recompute Exp convolution right7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S139 · premise_and_result_audit — Recompute Exp convolution right7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S138 · premise_and_result_audit — Recompute Exp convolution left7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S137 · premise_and_result_audit — Recompute Exp convolution left7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S136 · premise_and_result_audit — Recompute Exp convolution left7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S135 · premise_and_result_audit — Recompute Exp convolution left7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S134 · premise_and_result_audit — Recompute Exp convolution left7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Recompute Exp convolution left7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S132 · premise_and_result_audit — Recompute Exp convolution left7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Recompute Exp convolution numerator7 with exact rational arithmetic, not rounded decimals.
• S130 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S129 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S128 · premise_and_result_audit — Recompute Exp convolution coefficient term6 with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Recompute Exp convolution denominator6 with exact rational arithmetic, not rounded decimals.
• S126 · premise_and_result_audit — Recompute Exp convolution right6 factorial step7 with exact rational arithmetic, not rounded decimals.
• S125 · premise_and_result_audit — Recompute Exp convolution right6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S124 · premise_and_result_audit — Recompute Exp convolution right6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S123 · premise_and_result_audit — Recompute Exp convolution right6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S122 · premise_and_result_audit — Recompute Exp convolution right6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S121 · premise_and_result_audit — Recompute Exp convolution right6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S120 · premise_and_result_audit — Recompute Exp convolution right6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Recompute Exp convolution left6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S118 · premise_and_result_audit — Recompute Exp convolution left6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Recompute Exp convolution left6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S116 · premise_and_result_audit — Recompute Exp convolution left6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S115 · premise_and_result_audit — Recompute Exp convolution left6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S114 · premise_and_result_audit — Recompute Exp convolution left6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Recompute Exp convolution numerator6 with exact rational arithmetic, not rounded decimals.
• S112 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S111 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S110 · premise_and_result_audit — Recompute Exp convolution coefficient term5 with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Recompute Exp convolution denominator5 with exact rational arithmetic, not rounded decimals.
• S108 · premise_and_result_audit — Recompute Exp convolution right5 factorial step8 with exact rational arithmetic, not rounded decimals.
• S107 · premise_and_result_audit — Recompute Exp convolution right5 factorial step7 with exact rational arithmetic, not rounded decimals.
• S106 · premise_and_result_audit — Recompute Exp convolution right5 factorial step6 with exact rational arithmetic, not rounded decimals.
• S105 · premise_and_result_audit — Recompute Exp convolution right5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S104 · premise_and_result_audit — Recompute Exp convolution right5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S103 · premise_and_result_audit — Recompute Exp convolution right5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S102 · premise_and_result_audit — Recompute Exp convolution right5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S101 · premise_and_result_audit — Recompute Exp convolution right5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S100 · premise_and_result_audit — Recompute Exp convolution left5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S099 · premise_and_result_audit — Recompute Exp convolution left5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S098 · premise_and_result_audit — Recompute Exp convolution left5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Recompute Exp convolution left5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S096 · premise_and_result_audit — Recompute Exp convolution left5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S095 · premise_and_result_audit — Recompute Exp convolution numerator5 with exact rational arithmetic, not rounded decimals.
• S094 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S093 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S092 · premise_and_result_audit — Recompute Exp convolution coefficient term4 with exact rational arithmetic, not rounded decimals.
• S091 · premise_and_result_audit — Recompute Exp convolution denominator4 with exact rational arithmetic, not rounded decimals.
• S090 · premise_and_result_audit — Recompute Exp convolution right4 factorial step9 with exact rational arithmetic, not rounded decimals.
• S089 · premise_and_result_audit — Recompute Exp convolution right4 factorial step8 with exact rational arithmetic, not rounded decimals.
• S088 · premise_and_result_audit — Recompute Exp convolution right4 factorial step7 with exact rational arithmetic, not rounded decimals.
• S087 · premise_and_result_audit — Recompute Exp convolution right4 factorial step6 with exact rational arithmetic, not rounded decimals.
• S086 · premise_and_result_audit — Recompute Exp convolution right4 factorial step5 with exact rational arithmetic, not rounded decimals.
• S085 · premise_and_result_audit — Recompute Exp convolution right4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S084 · premise_and_result_audit — Recompute Exp convolution right4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S083 · premise_and_result_audit — Recompute Exp convolution right4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S082 · premise_and_result_audit — Recompute Exp convolution right4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S081 · premise_and_result_audit — Recompute Exp convolution left4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S080 · premise_and_result_audit — Recompute Exp convolution left4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S079 · premise_and_result_audit — Recompute Exp convolution left4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S078 · premise_and_result_audit — Recompute Exp convolution left4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S077 · premise_and_result_audit — Recompute Exp convolution numerator4 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 term3 with exact rational arithmetic, not rounded decimals.
• S073 · premise_and_result_audit — Recompute Exp convolution denominator3 with exact rational arithmetic, not rounded decimals.
• S072 · premise_and_result_audit — Recompute Exp convolution right3 factorial step10 with exact rational arithmetic, not rounded decimals.
• S071 · premise_and_result_audit — Recompute Exp convolution right3 factorial step9 with exact rational arithmetic, not rounded decimals.
• S070 · premise_and_result_audit — Recompute Exp convolution right3 factorial step8 with exact rational arithmetic, not rounded decimals.
• S069 · premise_and_result_audit — Recompute Exp convolution right3 factorial step7 with exact rational arithmetic, not rounded decimals.
• S068 · premise_and_result_audit — Recompute Exp convolution right3 factorial step6 with exact rational arithmetic, not rounded decimals.
• S067 · premise_and_result_audit — Recompute Exp convolution right3 factorial step5 with exact rational arithmetic, not rounded decimals.
• S066 · premise_and_result_audit — Recompute Exp convolution right3 factorial step4 with exact rational arithmetic, not rounded decimals.
• S065 · premise_and_result_audit — Recompute Exp convolution right3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S064 · premise_and_result_audit — Recompute Exp convolution right3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S063 · premise_and_result_audit — Recompute Exp convolution right3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S062 · premise_and_result_audit — Recompute Exp convolution left3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S061 · premise_and_result_audit — Recompute Exp convolution left3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S060 · premise_and_result_audit — Recompute Exp convolution left3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S059 · premise_and_result_audit — Recompute Exp convolution numerator3 with exact rational arithmetic, not rounded decimals.
• S058 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S057 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S056 · premise_and_result_audit — Recompute Exp convolution coefficient term2 with exact rational arithmetic, not rounded decimals.
• S055 · premise_and_result_audit — Recompute Exp convolution denominator2 with exact rational arithmetic, not rounded decimals.
• S054 · premise_and_result_audit — Recompute Exp convolution right2 factorial step11 with exact rational arithmetic, not rounded decimals.
• S053 · premise_and_result_audit — Recompute Exp convolution right2 factorial step10 with exact rational arithmetic, not rounded decimals.
• S052 · premise_and_result_audit — Recompute Exp convolution right2 factorial step9 with exact rational arithmetic, not rounded decimals.
• S051 · premise_and_result_audit — Recompute Exp convolution right2 factorial step8 with exact rational arithmetic, not rounded decimals.
• S050 · premise_and_result_audit — Recompute Exp convolution right2 factorial step7 with exact rational arithmetic, not rounded decimals.
• S049 · premise_and_result_audit — Recompute Exp convolution right2 factorial step6 with exact rational arithmetic, not rounded decimals.
• S048 · premise_and_result_audit — Recompute Exp convolution right2 factorial step5 with exact rational arithmetic, not rounded decimals.
• S047 · premise_and_result_audit — Recompute Exp convolution right2 factorial step4 with exact rational arithmetic, not rounded decimals.
• S046 · premise_and_result_audit — Recompute Exp convolution right2 factorial step3 with exact rational arithmetic, not rounded decimals.
• S045 · premise_and_result_audit — Recompute Exp convolution right2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S044 · premise_and_result_audit — Recompute Exp convolution right2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S043 · premise_and_result_audit — Recompute Exp convolution left2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S042 · premise_and_result_audit — Recompute Exp convolution left2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S041 · premise_and_result_audit — Recompute Exp convolution numerator2 with exact rational arithmetic, not rounded decimals.
• S040 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S039 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S038 · premise_and_result_audit — Recompute Exp convolution coefficient term1 with exact rational arithmetic, not rounded decimals.
• S037 · premise_and_result_audit — Recompute Exp convolution denominator1 with exact rational arithmetic, not rounded decimals.
• S036 · premise_and_result_audit — Recompute Exp convolution right1 factorial step12 with exact rational arithmetic, not rounded decimals.
• S035 · premise_and_result_audit — Recompute Exp convolution right1 factorial step11 with exact rational arithmetic, not rounded decimals.
• S034 · premise_and_result_audit — Recompute Exp convolution right1 factorial step10 with exact rational arithmetic, not rounded decimals.
• S033 · premise_and_result_audit — Recompute Exp convolution right1 factorial step9 with exact rational arithmetic, not rounded decimals.
• S032 · premise_and_result_audit — Recompute Exp convolution right1 factorial step8 with exact rational arithmetic, not rounded decimals.
• S031 · premise_and_result_audit — Recompute Exp convolution right1 factorial step7 with exact rational arithmetic, not rounded decimals.
• S030 · premise_and_result_audit — Recompute Exp convolution right1 factorial step6 with exact rational arithmetic, not rounded decimals.
• S029 · premise_and_result_audit — Recompute Exp convolution right1 factorial step5 with exact rational arithmetic, not rounded decimals.
• S028 · premise_and_result_audit — Recompute Exp convolution right1 factorial step4 with exact rational arithmetic, not rounded decimals.
• S027 · premise_and_result_audit — Recompute Exp convolution right1 factorial step3 with exact rational arithmetic, not rounded decimals.
• S026 · premise_and_result_audit — Recompute Exp convolution right1 factorial step2 with exact rational arithmetic, not rounded decimals.
• S025 · premise_and_result_audit — Recompute Exp convolution right1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S024 · premise_and_result_audit — Recompute Exp convolution left1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S023 · premise_and_result_audit — Recompute Exp convolution numerator1 with exact rational arithmetic, not rounded decimals.
• S022 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• 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 — Recompute Exp convolution coefficient term0 with exact rational arithmetic, not rounded decimals.
• S019 · premise_and_result_audit — Recompute Exp convolution denominator0 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

(14/15, -15/16, 13, [[0, -320361328125/4616297704445815291904], [1, 1423828125/1585267068834414592], [2, -132890625/24769797950537728], [3, 1378125/70368744177664], [4, -214375/4398046511104], [5, 12005/137438953472], [6, -16807/144955146240], [7, 117649/1019215872000], [8, -823543/9555148800000], [9, 5764801/120932352000000], [10, -40353607/2125764000000000], [11, 282475249/54804853125000000], [12, -1977326743/2312079741210937500], [13, 110730297608/1690708310760498046875]], -1/54579111145812232494907392000000000000000, -1/54579111145812232494907392000000000000000, 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.