Question 24216: 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=16/17, y=-17/18, declared degree=15. 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=16/17, y=-17/18, declared degree=15. 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]]

(16/17)^0

Exp convolution x power0 = 1

(-17/18)^15

Exp convolution y power15 = -2862423051509815793/6746640616477458432

Exp convolution numerator0 := mul(1, -2862423051509815793/6746640616477458432)

Exp convolution numerator0 = -2862423051509815793/6746640616477458432

source roles = [0]

derived = [1]

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

Exp convolution right0 factorial step1 = 1

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

Exp convolution right0 factorial step2 = 2

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

Exp convolution right0 factorial step3 = 6

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

Exp convolution right0 factorial step4 = 24

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

Exp convolution right0 factorial step5 = 120

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

Exp convolution right0 factorial step6 = 720

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

Exp convolution right0 factorial step7 = 5040

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

Exp convolution right0 factorial step8 = 40320

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

Exp convolution right0 factorial step9 = 362880

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

Exp convolution right0 factorial step10 = 3628800

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

Exp convolution right0 factorial step11 = 39916800

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

Exp convolution right0 factorial step12 = 479001600

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

Exp convolution right0 factorial step13 = 6227020800

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

Exp convolution right0 factorial step14 = 87178291200

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

Exp convolution right0 factorial step15 = 1307674368000

Exp convolution denominator0 := mul(1, 1307674368000)

Exp convolution denominator0 = 1307674368000

Exp convolution coefficient term0 := div(-2862423051509815793/6746640616477458432, 1307674368000)

Exp convolution coefficient term0 = -2862423051509815793/8822409004275290841311870976000

(16/17)^1

Exp convolution x power1 = 16/17

(-17/18)^14

Exp convolution y power14 = 168377826559400929/374813367582081024

Exp convolution numerator1 := mul(16/17, 168377826559400929/374813367582081024)

Exp convolution numerator1 = 9904578032905937/23425835473880064

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

Exp convolution left1 factorial step1 = 1

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

Exp convolution right1 factorial step1 = 1

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

Exp convolution right1 factorial step2 = 2

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

Exp convolution right1 factorial step3 = 6

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

Exp convolution right1 factorial step4 = 24

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

Exp convolution right1 factorial step5 = 120

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

Exp convolution right1 factorial step6 = 720

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

Exp convolution right1 factorial step7 = 5040

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

Exp convolution right1 factorial step8 = 40320

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

Exp convolution right1 factorial step9 = 362880

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

Exp convolution right1 factorial step10 = 3628800

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

Exp convolution right1 factorial step11 = 39916800

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

Exp convolution right1 factorial step12 = 479001600

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

Exp convolution right1 factorial step13 = 6227020800

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

Exp convolution right1 factorial step14 = 87178291200

Exp convolution denominator1 := mul(1, 87178291200)

Exp convolution denominator1 = 87178291200

Exp convolution coefficient term1 := div(9904578032905937/23425835473880064, 87178291200)

Exp convolution coefficient term1 = 9904578032905937/2042224306545206213266636800

(16/17)^2

Exp convolution x power2 = 256/289

(-17/18)^13

Exp convolution y power13 = -9904578032905937/20822964865671168

Exp convolution numerator2 := mul(256/289, -9904578032905937/20822964865671168)

Exp convolution numerator2 = -34271896307633/81339706506528

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

Exp convolution left2 factorial step1 = 1

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

Exp convolution left2 factorial step2 = 2

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

Exp convolution right2 factorial step1 = 1

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

Exp convolution right2 factorial step2 = 2

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

Exp convolution right2 factorial step3 = 6

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

Exp convolution right2 factorial step4 = 24

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

Exp convolution right2 factorial step5 = 120

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

Exp convolution right2 factorial step6 = 720

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

Exp convolution right2 factorial step7 = 5040

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

Exp convolution right2 factorial step8 = 40320

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

Exp convolution right2 factorial step9 = 362880

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

Exp convolution right2 factorial step10 = 3628800

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

Exp convolution right2 factorial step11 = 39916800

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

Exp convolution right2 factorial step12 = 479001600

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

Exp convolution right2 factorial step13 = 6227020800

Exp convolution denominator2 := mul(2, 6227020800)

Exp convolution denominator2 = 12454041600

Exp convolution coefficient term2 := div(-34271896307633/81339706506528, 12454041600)

Exp convolution coefficient term2 = -34271896307633/1013008088564090383564800

(16/17)^3

Exp convolution x power3 = 4096/4913

(-17/18)^12

Exp convolution y power12 = 582622237229761/1156831381426176

Exp convolution numerator3 := mul(4096/4913, 582622237229761/1156831381426176)

Exp convolution numerator3 = 118587876497/282429536481

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

Exp convolution left3 factorial step1 = 1

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

Exp convolution left3 factorial step2 = 2

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

Exp convolution left3 factorial step3 = 6

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

Exp convolution right3 factorial step1 = 1

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

Exp convolution right3 factorial step2 = 2

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

Exp convolution right3 factorial step3 = 6

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

Exp convolution right3 factorial step4 = 24

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

Exp convolution right3 factorial step5 = 120

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

Exp convolution right3 factorial step6 = 720

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

Exp convolution right3 factorial step7 = 5040

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

Exp convolution right3 factorial step8 = 40320

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

Exp convolution right3 factorial step9 = 362880

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

Exp convolution right3 factorial step10 = 3628800

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

Exp convolution right3 factorial step11 = 39916800

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

Exp convolution right3 factorial step12 = 479001600

Exp convolution denominator3 := mul(6, 479001600)

Exp convolution denominator3 = 2874009600

Exp convolution coefficient term3 := div(118587876497/282429536481, 2874009600)

Exp convolution coefficient term3 = 118587876497/811705199169944217600

(16/17)^4

Exp convolution x power4 = 65536/83521

(-17/18)^11

Exp convolution y power11 = -34271896307633/64268410079232

Exp convolution numerator4 := mul(65536/83521, -34271896307633/64268410079232)

Exp convolution numerator4 = -13130837536/31381059609

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

Exp convolution left4 factorial step1 = 1

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

Exp convolution left4 factorial step2 = 2

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

Exp convolution left4 factorial step3 = 6

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

Exp convolution left4 factorial step4 = 24

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

Exp convolution right4 factorial step1 = 1

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

Exp convolution right4 factorial step2 = 2

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

Exp convolution right4 factorial step3 = 6

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

Exp convolution right4 factorial step4 = 24

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

Exp convolution right4 factorial step5 = 120

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

Exp convolution right4 factorial step6 = 720

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

Exp convolution right4 factorial step7 = 5040

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

Exp convolution right4 factorial step8 = 40320

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

Exp convolution right4 factorial step9 = 362880

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

Exp convolution right4 factorial step10 = 3628800

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

Exp convolution right4 factorial step11 = 39916800

Exp convolution denominator4 := mul(24, 39916800)

Exp convolution denominator4 = 958003200

Exp convolution coefficient term4 := div(-13130837536/31381059609, 958003200)

Exp convolution coefficient term4 = -410338673/939473610150398400

(16/17)^5

Exp convolution x power5 = 1048576/1419857

(-17/18)^10

Exp convolution y power10 = 2015993900449/3570467226624

Exp convolution numerator5 := mul(1048576/1419857, 2015993900449/3570467226624)

Exp convolution numerator5 = 1453933568/3486784401

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

Exp convolution left5 factorial step1 = 1

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

Exp convolution left5 factorial step2 = 2

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

Exp convolution left5 factorial step3 = 6

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

Exp convolution left5 factorial step4 = 24

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

Exp convolution left5 factorial step5 = 120

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

Exp convolution right5 factorial step1 = 1

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

Exp convolution right5 factorial step2 = 2

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

Exp convolution right5 factorial step3 = 6

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

Exp convolution right5 factorial step4 = 24

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

Exp convolution right5 factorial step5 = 120

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

Exp convolution right5 factorial step6 = 720

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

Exp convolution right5 factorial step7 = 5040

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

Exp convolution right5 factorial step8 = 40320

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

Exp convolution right5 factorial step9 = 362880

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

Exp convolution right5 factorial step10 = 3628800

Exp convolution denominator5 := mul(120, 3628800)

Exp convolution denominator5 = 435456000

Exp convolution coefficient term5 := div(1453933568/3486784401, 435456000)

Exp convolution coefficient term5 = 1419857/1482755066525250

(16/17)^6

Exp convolution x power6 = 16777216/24137569

(-17/18)^9

Exp convolution y power9 = -118587876497/198359290368

Exp convolution numerator6 := mul(16777216/24137569, -118587876497/198359290368)

Exp convolution numerator6 = -160989184/387420489

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

Exp convolution left6 factorial step1 = 1

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

Exp convolution left6 factorial step2 = 2

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

Exp convolution left6 factorial step3 = 6

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

Exp convolution left6 factorial step4 = 24

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

Exp convolution left6 factorial step5 = 120

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

Exp convolution left6 factorial step6 = 720

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

Exp convolution right6 factorial step1 = 1

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

Exp convolution right6 factorial step2 = 2

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

Exp convolution right6 factorial step3 = 6

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

Exp convolution right6 factorial step4 = 24

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

Exp convolution right6 factorial step5 = 120

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

Exp convolution right6 factorial step6 = 720

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

Exp convolution right6 factorial step7 = 5040

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

Exp convolution right6 factorial step8 = 40320

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

Exp convolution right6 factorial step9 = 362880

Exp convolution denominator6 := mul(720, 362880)

Exp convolution denominator6 = 261273600

Exp convolution coefficient term6 := div(-160989184/387420489, 261273600)

Exp convolution coefficient term6 = -78608/49425168884175

(16/17)^7

Exp convolution x power7 = 268435456/410338673

(-17/18)^8

Exp convolution y power8 = 6975757441/11019960576

Exp convolution numerator7 := mul(268435456/410338673, 6975757441/11019960576)

Exp convolution numerator7 = 17825792/43046721

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

Exp convolution left7 factorial step1 = 1

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

Exp convolution left7 factorial step2 = 2

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

Exp convolution left7 factorial step3 = 6

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

Exp convolution left7 factorial step4 = 24

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

Exp convolution left7 factorial step5 = 120

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

Exp convolution left7 factorial step6 = 720

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

Exp convolution left7 factorial step7 = 5040

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

Exp convolution right7 factorial step1 = 1

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

Exp convolution right7 factorial step2 = 2

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

Exp convolution right7 factorial step3 = 6

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

Exp convolution right7 factorial step4 = 24

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

Exp convolution right7 factorial step5 = 120

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

Exp convolution right7 factorial step6 = 720

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

Exp convolution right7 factorial step7 = 5040

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

Exp convolution right7 factorial step8 = 40320

Exp convolution denominator7 := mul(5040, 40320)

Exp convolution denominator7 = 203212800

Exp convolution coefficient term7 := div(17825792/43046721, 203212800)

Exp convolution coefficient term7 = 8704/4271310891225

(16/17)^8

Exp convolution x power8 = 4294967296/6975757441

(-17/18)^7

Exp convolution y power7 = -410338673/612220032

Exp convolution numerator8 := mul(4294967296/6975757441, -410338673/612220032)

Exp convolution numerator8 = -33554432/81310473

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

Exp convolution left8 factorial step1 = 1

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

Exp convolution left8 factorial step2 = 2

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

Exp convolution left8 factorial step3 = 6

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

Exp convolution left8 factorial step4 = 24

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

Exp convolution left8 factorial step5 = 120

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

Exp convolution left8 factorial step6 = 720

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

Exp convolution left8 factorial step7 = 5040

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

Exp convolution left8 factorial step8 = 40320

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

Exp convolution right8 factorial step1 = 1

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

Exp convolution right8 factorial step2 = 2

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

Exp convolution right8 factorial step3 = 6

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

Exp convolution right8 factorial step4 = 24

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

Exp convolution right8 factorial step5 = 120

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

Exp convolution right8 factorial step6 = 720

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

Exp convolution right8 factorial step7 = 5040

Exp convolution denominator8 := mul(40320, 5040)

Exp convolution denominator8 = 203212800

Exp convolution coefficient term8 := div(-33554432/81310473, 203212800)

Exp convolution coefficient term8 = -16384/8068031683425

(16/17)^9

Exp convolution x power9 = 68719476736/118587876497

(-17/18)^6

Exp convolution y power6 = 24137569/34012224

Exp convolution numerator9 := mul(68719476736/118587876497, 24137569/34012224)

Exp convolution numerator9 = 1073741824/2610969633

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

Exp convolution left9 factorial step1 = 1

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

Exp convolution left9 factorial step2 = 2

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

Exp convolution left9 factorial step3 = 6

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

Exp convolution left9 factorial step4 = 24

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

Exp convolution left9 factorial step5 = 120

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

Exp convolution left9 factorial step6 = 720

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

Exp convolution left9 factorial step7 = 5040

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

Exp convolution left9 factorial step8 = 40320

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

Exp convolution left9 factorial step9 = 362880

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

Exp convolution right9 factorial step1 = 1

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

Exp convolution right9 factorial step2 = 2

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

Exp convolution right9 factorial step3 = 6

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

Exp convolution right9 factorial step4 = 24

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

Exp convolution right9 factorial step5 = 120

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

Exp convolution right9 factorial step6 = 720

Exp convolution denominator9 := mul(362880, 720)

Exp convolution denominator9 = 261273600

Exp convolution coefficient term9 := div(1073741824/2610969633, 261273600)

Exp convolution coefficient term9 = 524288/333094450929975

(16/17)^10

Exp convolution x power10 = 1099511627776/2015993900449

(-17/18)^5

Exp convolution y power5 = -1419857/1889568

Exp convolution numerator10 := mul(1099511627776/2015993900449, -1419857/1889568)

Exp convolution numerator10 = -34359738368/83841135993

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

Exp convolution left10 factorial step1 = 1

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

Exp convolution left10 factorial step2 = 2

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

Exp convolution left10 factorial step3 = 6

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

Exp convolution left10 factorial step4 = 24

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

Exp convolution left10 factorial step5 = 120

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

Exp convolution left10 factorial step6 = 720

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

Exp convolution left10 factorial step7 = 5040

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

Exp convolution left10 factorial step8 = 40320

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

Exp convolution left10 factorial step9 = 362880

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

Exp convolution left10 factorial step10 = 3628800

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

Exp convolution right10 factorial step1 = 1

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

Exp convolution right10 factorial step2 = 2

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

Exp convolution right10 factorial step3 = 6

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

Exp convolution right10 factorial step4 = 24

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

Exp convolution right10 factorial step5 = 120

Exp convolution denominator10 := mul(3628800, 120)

Exp convolution denominator10 = 435456000

Exp convolution coefficient term10 := div(-34359738368/83841135993, 435456000)

Exp convolution coefficient term10 = -16777216/17826721540511625

(16/17)^11

Exp convolution x power11 = 17592186044416/34271896307633

(-17/18)^4

Exp convolution y power4 = 83521/104976

Exp convolution numerator11 := mul(17592186044416/34271896307633, 83521/104976)

Exp convolution numerator11 = 1099511627776/2692232033553

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

Exp convolution left11 factorial step1 = 1

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

Exp convolution left11 factorial step2 = 2

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

Exp convolution left11 factorial step3 = 6

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

Exp convolution left11 factorial step4 = 24

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

Exp convolution left11 factorial step5 = 120

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

Exp convolution left11 factorial step6 = 720

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

Exp convolution left11 factorial step7 = 5040

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

Exp convolution left11 factorial step8 = 40320

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

Exp convolution left11 factorial step9 = 362880

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

Exp convolution left11 factorial step10 = 3628800

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

Exp convolution left11 factorial step11 = 39916800

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

Exp convolution right11 factorial step1 = 1

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

Exp convolution right11 factorial step2 = 2

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

Exp convolution right11 factorial step3 = 6

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

Exp convolution right11 factorial step4 = 24

Exp convolution denominator11 := mul(39916800, 24)

Exp convolution denominator11 = 958003200

Exp convolution coefficient term11 := div(1099511627776/2692232033553, 958003200)

Exp convolution coefficient term11 = 536870912/1259358839495254575

(16/17)^12

Exp convolution x power12 = 281474976710656/582622237229761

(-17/18)^3

Exp convolution y power3 = -4913/5832

Exp convolution numerator12 := mul(281474976710656/582622237229761, -4913/5832)

Exp convolution numerator12 = -35184372088832/86450561966313

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

Exp convolution left12 factorial step1 = 1

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

Exp convolution left12 factorial step2 = 2

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

Exp convolution left12 factorial step3 = 6

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

Exp convolution left12 factorial step4 = 24

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

Exp convolution left12 factorial step5 = 120

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

Exp convolution left12 factorial step6 = 720

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

Exp convolution left12 factorial step7 = 5040

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

Exp convolution left12 factorial step8 = 40320

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

Exp convolution left12 factorial step9 = 362880

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

Exp convolution left12 factorial step10 = 3628800

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

Exp convolution left12 factorial step11 = 39916800

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

Exp convolution left12 factorial step12 = 479001600

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

Exp convolution right12 factorial step1 = 1

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

Exp convolution right12 factorial step2 = 2

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

Exp convolution right12 factorial step3 = 6

Exp convolution denominator12 := mul(479001600, 6)

Exp convolution denominator12 = 2874009600

Exp convolution coefficient term12 := div(-35184372088832/86450561966313, 2874009600)

Exp convolution coefficient term12 = -17179869184/121318234871376190725

(16/17)^13

Exp convolution x power13 = 4503599627370496/9904578032905937

(-17/18)^2

Exp convolution y power2 = 289/324

Exp convolution numerator13 := mul(4503599627370496/9904578032905937, 289/324)

Exp convolution numerator13 = 1125899906842624/2776023600918273

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

Exp convolution left13 factorial step1 = 1

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

Exp convolution left13 factorial step2 = 2

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

Exp convolution left13 factorial step3 = 6

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

Exp convolution left13 factorial step4 = 24

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

Exp convolution left13 factorial step5 = 120

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

Exp convolution left13 factorial step6 = 720

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

Exp convolution left13 factorial step7 = 5040

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

Exp convolution left13 factorial step8 = 40320

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

Exp convolution left13 factorial step9 = 362880

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

Exp convolution left13 factorial step10 = 3628800

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

Exp convolution left13 factorial step11 = 39916800

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

Exp convolution left13 factorial step12 = 479001600

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

Exp convolution left13 factorial step13 = 6227020800

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

Exp convolution right13 factorial step1 = 1

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

Exp convolution right13 factorial step2 = 2

Exp convolution denominator13 := mul(6227020800, 2)

Exp convolution denominator13 = 12454041600

Exp convolution coefficient term13 := div(1125899906842624/2776023600918273, 12454041600)

Exp convolution coefficient term13 = 549755813888/16881207718954086983475

(16/17)^14

Exp convolution x power14 = 72057594037927936/168377826559400929

(-17/18)^1

Exp convolution y power1 = -17/18

Exp convolution numerator14 := mul(72057594037927936/168377826559400929, -17/18)

Exp convolution numerator14 = -36028797018963968/89141202296153433

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

Exp convolution left14 factorial step1 = 1

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

Exp convolution left14 factorial step2 = 2

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

Exp convolution left14 factorial step3 = 6

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

Exp convolution left14 factorial step4 = 24

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

Exp convolution left14 factorial step5 = 120

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

Exp convolution left14 factorial step6 = 720

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

Exp convolution left14 factorial step7 = 5040

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

Exp convolution left14 factorial step8 = 40320

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

Exp convolution left14 factorial step9 = 362880

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

Exp convolution left14 factorial step10 = 3628800

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

Exp convolution left14 factorial step11 = 39916800

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

Exp convolution left14 factorial step12 = 479001600

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

Exp convolution left14 factorial step13 = 6227020800

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

Exp convolution left14 factorial step14 = 87178291200

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

Exp convolution right14 factorial step1 = 1

Exp convolution denominator14 := mul(87178291200, 1)

Exp convolution denominator14 = 87178291200

Exp convolution coefficient term14 := div(-36028797018963968/89141202296153433, 87178291200)

Exp convolution coefficient term14 = -17592186044416/3794520357271568663063325

(16/17)^15

Exp convolution x power15 = 1152921504606846976/2862423051509815793

(-17/18)^0

Exp convolution y power0 = 1

Exp convolution numerator15 := mul(1152921504606846976/2862423051509815793, 1)

Exp convolution numerator15 = 1152921504606846976/2862423051509815793

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

Exp convolution left15 factorial step1 = 1

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

Exp convolution left15 factorial step2 = 2

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

Exp convolution left15 factorial step3 = 6

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

Exp convolution left15 factorial step4 = 24

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

Exp convolution left15 factorial step5 = 120

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

Exp convolution left15 factorial step6 = 720

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

Exp convolution left15 factorial step7 = 5040

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

Exp convolution left15 factorial step8 = 40320

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

Exp convolution left15 factorial step9 = 362880

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

Exp convolution left15 factorial step10 = 3628800

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

Exp convolution left15 factorial step11 = 39916800

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

Exp convolution left15 factorial step12 = 479001600

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

Exp convolution left15 factorial step13 = 6227020800

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

Exp convolution left15 factorial step14 = 87178291200

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

Exp convolution left15 factorial step15 = 1307674368000

source roles = [0]

derived = [1]

Exp convolution denominator15 := mul(1307674368000, 1)

Exp convolution denominator15 = 1307674368000

Exp convolution coefficient term15 := div(1152921504606846976/2862423051509815793, 1307674368000)

Exp convolution coefficient term15 = 562949953421312/1827693972085805572708834875

Exp complete declared-degree convolution := sum(-2862423051509815793/8822409004275290841311870976000, 9904578032905937/2042224306545206213266636800, -34271896307633/1013008088564090383564800, 118587876497/811705199169944217600, -410338673/939473610150398400, 1419857/1482755066525250, -78608/49425168884175, 8704/4271310891225, -16384/8068031683425, 524288/333094450929975, -16777216/17826721540511625, 536870912/1259358839495254575, -17179869184/121318234871376190725, 549755813888/16881207718954086983475, -17592186044416/3794520357271568663063325, 562949953421312/1827693972085805572708834875)

Exp complete declared-degree convolution = -1/25253466903685353496585230352209316437943123968000

Exp ORIGINAL arguments sum := sum(16/17, -17/18)

Exp ORIGINAL arguments sum = -1/306

(-1/306)^15

Exp sum argument declared power = -1/19311739620857471373626580369134616576

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

Exp sum argument factorial step1 = 1

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

Exp sum argument factorial step2 = 2

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

Exp sum argument factorial step3 = 6

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

Exp sum argument factorial step4 = 24

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

Exp sum argument factorial step5 = 120

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

Exp sum argument factorial step6 = 720

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

Exp sum argument factorial step7 = 5040

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

Exp sum argument factorial step8 = 40320

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

Exp sum argument factorial step9 = 362880

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

Exp sum argument factorial step10 = 3628800

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

Exp sum argument factorial step11 = 39916800

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

Exp sum argument factorial step12 = 479001600

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

Exp sum argument factorial step13 = 6227020800

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

Exp sum argument factorial step14 = 87178291200

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

Exp sum argument factorial step15 = 1307674368000

Exp sum argument coefficient := div(-1/19311739620857471373626580369134616576, 1307674368000)

Exp sum argument coefficient = -1/25253466903685353496585230352209316437943123968000

source roles = [[16/17, -17/18], 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 = [[16/17, -17/18, 15], 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

• S344 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S343 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S342 · premise_and_result_audit — Recompute Exp sum argument coefficient with exact rational arithmetic, not rounded decimals.
• S341 · premise_and_result_audit — Recompute Exp sum argument factorial step15 with exact rational arithmetic, not rounded decimals.
• S340 · premise_and_result_audit — Recompute Exp sum argument factorial step14 with exact rational arithmetic, not rounded decimals.
• S339 · premise_and_result_audit — Recompute Exp sum argument factorial step13 with exact rational arithmetic, not rounded decimals.
• S338 · premise_and_result_audit — Recompute Exp sum argument factorial step12 with exact rational arithmetic, not rounded decimals.
• S337 · premise_and_result_audit — Recompute Exp sum argument factorial step11 with exact rational arithmetic, not rounded decimals.
• S336 · premise_and_result_audit — Recompute Exp sum argument factorial step10 with exact rational arithmetic, not rounded decimals.
• S335 · premise_and_result_audit — Recompute Exp sum argument factorial step9 with exact rational arithmetic, not rounded decimals.
• S334 · premise_and_result_audit — Recompute Exp sum argument factorial step8 with exact rational arithmetic, not rounded decimals.
• S333 · premise_and_result_audit — Recompute Exp sum argument factorial step7 with exact rational arithmetic, not rounded decimals.
• S332 · premise_and_result_audit — Recompute Exp sum argument factorial step6 with exact rational arithmetic, not rounded decimals.
• S331 · premise_and_result_audit — Recompute Exp sum argument factorial step5 with exact rational arithmetic, not rounded decimals.
• S330 · premise_and_result_audit — Recompute Exp sum argument factorial step4 with exact rational arithmetic, not rounded decimals.
• S329 · premise_and_result_audit — Recompute Exp sum argument factorial step3 with exact rational arithmetic, not rounded decimals.
• S328 · premise_and_result_audit — Recompute Exp sum argument factorial step2 with exact rational arithmetic, not rounded decimals.
• S327 · premise_and_result_audit — Recompute Exp sum argument factorial step1 with exact rational arithmetic, not rounded decimals.
• S326 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S325 · premise_and_result_audit — Recompute Exp ORIGINAL arguments sum with exact rational arithmetic, not rounded decimals.
• S324 · premise_and_result_audit — Recompute Exp complete declared-degree convolution with exact rational arithmetic, not rounded decimals.
• S323 · premise_and_result_audit — Recompute Exp convolution coefficient term15 with exact rational arithmetic, not rounded decimals.
• S322 · premise_and_result_audit — Recompute Exp convolution denominator15 with exact rational arithmetic, not rounded decimals.
• S321 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S320 · premise_and_result_audit — Recompute Exp convolution left15 factorial step15 with exact rational arithmetic, not rounded decimals.
• S319 · premise_and_result_audit — Recompute Exp convolution left15 factorial step14 with exact rational arithmetic, not rounded decimals.
• S318 · premise_and_result_audit — Recompute Exp convolution left15 factorial step13 with exact rational arithmetic, not rounded decimals.
• S317 · premise_and_result_audit — Recompute Exp convolution left15 factorial step12 with exact rational arithmetic, not rounded decimals.
• S316 · premise_and_result_audit — Recompute Exp convolution left15 factorial step11 with exact rational arithmetic, not rounded decimals.
• S315 · premise_and_result_audit — Recompute Exp convolution left15 factorial step10 with exact rational arithmetic, not rounded decimals.
• S314 · premise_and_result_audit — Recompute Exp convolution left15 factorial step9 with exact rational arithmetic, not rounded decimals.
• S313 · premise_and_result_audit — Recompute Exp convolution left15 factorial step8 with exact rational arithmetic, not rounded decimals.
• S312 · premise_and_result_audit — Recompute Exp convolution left15 factorial step7 with exact rational arithmetic, not rounded decimals.
• S311 · premise_and_result_audit — Recompute Exp convolution left15 factorial step6 with exact rational arithmetic, not rounded decimals.
• S310 · premise_and_result_audit — Recompute Exp convolution left15 factorial step5 with exact rational arithmetic, not rounded decimals.
• S309 · premise_and_result_audit — Recompute Exp convolution left15 factorial step4 with exact rational arithmetic, not rounded decimals.
• S308 · premise_and_result_audit — Recompute Exp convolution left15 factorial step3 with exact rational arithmetic, not rounded decimals.
• S307 · premise_and_result_audit — Recompute Exp convolution left15 factorial step2 with exact rational arithmetic, not rounded decimals.
• S306 · premise_and_result_audit — Recompute Exp convolution left15 factorial step1 with exact rational arithmetic, not rounded decimals.
• S305 · premise_and_result_audit — Recompute Exp convolution numerator15 with exact rational arithmetic, not rounded decimals.
• S304 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S303 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S302 · premise_and_result_audit — Recompute Exp convolution coefficient term14 with exact rational arithmetic, not rounded decimals.
• S301 · premise_and_result_audit — Recompute Exp convolution denominator14 with exact rational arithmetic, not rounded decimals.
• S300 · premise_and_result_audit — Recompute Exp convolution right14 factorial step1 with exact rational arithmetic, not rounded decimals.
• S299 · premise_and_result_audit — Recompute Exp convolution left14 factorial step14 with exact rational arithmetic, not rounded decimals.
• S298 · premise_and_result_audit — Recompute Exp convolution left14 factorial step13 with exact rational arithmetic, not rounded decimals.
• S297 · premise_and_result_audit — Recompute Exp convolution left14 factorial step12 with exact rational arithmetic, not rounded decimals.
• S296 · premise_and_result_audit — Recompute Exp convolution left14 factorial step11 with exact rational arithmetic, not rounded decimals.
• S295 · premise_and_result_audit — Recompute Exp convolution left14 factorial step10 with exact rational arithmetic, not rounded decimals.
• S294 · premise_and_result_audit — Recompute Exp convolution left14 factorial step9 with exact rational arithmetic, not rounded decimals.
• S293 · premise_and_result_audit — Recompute Exp convolution left14 factorial step8 with exact rational arithmetic, not rounded decimals.
• S292 · premise_and_result_audit — Recompute Exp convolution left14 factorial step7 with exact rational arithmetic, not rounded decimals.
• S291 · premise_and_result_audit — Recompute Exp convolution left14 factorial step6 with exact rational arithmetic, not rounded decimals.
• S290 · premise_and_result_audit — Recompute Exp convolution left14 factorial step5 with exact rational arithmetic, not rounded decimals.
• S289 · premise_and_result_audit — Recompute Exp convolution left14 factorial step4 with exact rational arithmetic, not rounded decimals.
• S288 · premise_and_result_audit — Recompute Exp convolution left14 factorial step3 with exact rational arithmetic, not rounded decimals.
• S287 · premise_and_result_audit — Recompute Exp convolution left14 factorial step2 with exact rational arithmetic, not rounded decimals.
• S286 · premise_and_result_audit — Recompute Exp convolution left14 factorial step1 with exact rational arithmetic, not rounded decimals.
• S285 · premise_and_result_audit — Recompute Exp convolution numerator14 with exact rational arithmetic, not rounded decimals.
• S284 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S283 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S282 · premise_and_result_audit — Recompute Exp convolution coefficient term13 with exact rational arithmetic, not rounded decimals.
• S281 · premise_and_result_audit — Recompute Exp convolution denominator13 with exact rational arithmetic, not rounded decimals.
• S280 · premise_and_result_audit — Recompute Exp convolution right13 factorial step2 with exact rational arithmetic, not rounded decimals.
• S279 · premise_and_result_audit — Recompute Exp convolution right13 factorial step1 with exact rational arithmetic, not rounded decimals.
• S278 · premise_and_result_audit — Recompute Exp convolution left13 factorial step13 with exact rational arithmetic, not rounded decimals.
• S277 · premise_and_result_audit — Recompute Exp convolution left13 factorial step12 with exact rational arithmetic, not rounded decimals.
• S276 · premise_and_result_audit — Recompute Exp convolution left13 factorial step11 with exact rational arithmetic, not rounded decimals.
• S275 · premise_and_result_audit — Recompute Exp convolution left13 factorial step10 with exact rational arithmetic, not rounded decimals.
• S274 · premise_and_result_audit — Recompute Exp convolution left13 factorial step9 with exact rational arithmetic, not rounded decimals.
• S273 · premise_and_result_audit — Recompute Exp convolution left13 factorial step8 with exact rational arithmetic, not rounded decimals.
• S272 · premise_and_result_audit — Recompute Exp convolution left13 factorial step7 with exact rational arithmetic, not rounded decimals.
• S271 · premise_and_result_audit — Recompute Exp convolution left13 factorial step6 with exact rational arithmetic, not rounded decimals.
• S270 · premise_and_result_audit — Recompute Exp convolution left13 factorial step5 with exact rational arithmetic, not rounded decimals.
• S269 · premise_and_result_audit — Recompute Exp convolution left13 factorial step4 with exact rational arithmetic, not rounded decimals.
• S268 · premise_and_result_audit — Recompute Exp convolution left13 factorial step3 with exact rational arithmetic, not rounded decimals.
• S267 · premise_and_result_audit — Recompute Exp convolution left13 factorial step2 with exact rational arithmetic, not rounded decimals.
• S266 · premise_and_result_audit — Recompute Exp convolution left13 factorial step1 with exact rational arithmetic, not rounded decimals.
• S265 · premise_and_result_audit — Recompute Exp convolution numerator13 with exact rational arithmetic, not rounded decimals.
• S264 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S263 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S262 · premise_and_result_audit — Recompute Exp convolution coefficient term12 with exact rational arithmetic, not rounded decimals.
• S261 · premise_and_result_audit — Recompute Exp convolution denominator12 with exact rational arithmetic, not rounded decimals.
• S260 · premise_and_result_audit — Recompute Exp convolution right12 factorial step3 with exact rational arithmetic, not rounded decimals.
• S259 · premise_and_result_audit — Recompute Exp convolution right12 factorial step2 with exact rational arithmetic, not rounded decimals.
• S258 · premise_and_result_audit — Recompute Exp convolution right12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S257 · premise_and_result_audit — Recompute Exp convolution left12 factorial step12 with exact rational arithmetic, not rounded decimals.
• S256 · premise_and_result_audit — Recompute Exp convolution left12 factorial step11 with exact rational arithmetic, not rounded decimals.
• S255 · premise_and_result_audit — Recompute Exp convolution left12 factorial step10 with exact rational arithmetic, not rounded decimals.
• S254 · premise_and_result_audit — Recompute Exp convolution left12 factorial step9 with exact rational arithmetic, not rounded decimals.
• S253 · premise_and_result_audit — Recompute Exp convolution left12 factorial step8 with exact rational arithmetic, not rounded decimals.
• S252 · premise_and_result_audit — Recompute Exp convolution left12 factorial step7 with exact rational arithmetic, not rounded decimals.
• S251 · premise_and_result_audit — Recompute Exp convolution left12 factorial step6 with exact rational arithmetic, not rounded decimals.
• S250 · premise_and_result_audit — Recompute Exp convolution left12 factorial step5 with exact rational arithmetic, not rounded decimals.
• S249 · premise_and_result_audit — Recompute Exp convolution left12 factorial step4 with exact rational arithmetic, not rounded decimals.
• S248 · premise_and_result_audit — Recompute Exp convolution left12 factorial step3 with exact rational arithmetic, not rounded decimals.
• S247 · premise_and_result_audit — Recompute Exp convolution left12 factorial step2 with exact rational arithmetic, not rounded decimals.
• S246 · premise_and_result_audit — Recompute Exp convolution left12 factorial step1 with exact rational arithmetic, not rounded decimals.
• S245 · premise_and_result_audit — Recompute Exp convolution numerator12 with exact rational arithmetic, not rounded decimals.
• S244 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S243 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S242 · premise_and_result_audit — Recompute Exp convolution coefficient term11 with exact rational arithmetic, not rounded decimals.
• S241 · premise_and_result_audit — Recompute Exp convolution denominator11 with exact rational arithmetic, not rounded decimals.
• S240 · premise_and_result_audit — Recompute Exp convolution right11 factorial step4 with exact rational arithmetic, not rounded decimals.
• S239 · premise_and_result_audit — Recompute Exp convolution right11 factorial step3 with exact rational arithmetic, not rounded decimals.
• S238 · premise_and_result_audit — Recompute Exp convolution right11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S237 · premise_and_result_audit — Recompute Exp convolution right11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S236 · premise_and_result_audit — Recompute Exp convolution left11 factorial step11 with exact rational arithmetic, not rounded decimals.
• S235 · premise_and_result_audit — Recompute Exp convolution left11 factorial step10 with exact rational arithmetic, not rounded decimals.
• S234 · premise_and_result_audit — Recompute Exp convolution left11 factorial step9 with exact rational arithmetic, not rounded decimals.
• S233 · premise_and_result_audit — Recompute Exp convolution left11 factorial step8 with exact rational arithmetic, not rounded decimals.
• S232 · premise_and_result_audit — Recompute Exp convolution left11 factorial step7 with exact rational arithmetic, not rounded decimals.
• S231 · premise_and_result_audit — Recompute Exp convolution left11 factorial step6 with exact rational arithmetic, not rounded decimals.
• S230 · premise_and_result_audit — Recompute Exp convolution left11 factorial step5 with exact rational arithmetic, not rounded decimals.
• S229 · premise_and_result_audit — Recompute Exp convolution left11 factorial step4 with exact rational arithmetic, not rounded decimals.
• S228 · premise_and_result_audit — Recompute Exp convolution left11 factorial step3 with exact rational arithmetic, not rounded decimals.
• S227 · premise_and_result_audit — Recompute Exp convolution left11 factorial step2 with exact rational arithmetic, not rounded decimals.
• S226 · premise_and_result_audit — Recompute Exp convolution left11 factorial step1 with exact rational arithmetic, not rounded decimals.
• S225 · premise_and_result_audit — Recompute Exp convolution numerator11 with exact rational arithmetic, not rounded decimals.
• S224 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S223 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S222 · premise_and_result_audit — Recompute Exp convolution coefficient term10 with exact rational arithmetic, not rounded decimals.
• S221 · premise_and_result_audit — Recompute Exp convolution denominator10 with exact rational arithmetic, not rounded decimals.
• S220 · premise_and_result_audit — Recompute Exp convolution right10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S219 · premise_and_result_audit — Recompute Exp convolution right10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S218 · premise_and_result_audit — Recompute Exp convolution right10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S217 · premise_and_result_audit — Recompute Exp convolution right10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S216 · premise_and_result_audit — Recompute Exp convolution right10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S215 · premise_and_result_audit — Recompute Exp convolution left10 factorial step10 with exact rational arithmetic, not rounded decimals.
• S214 · premise_and_result_audit — Recompute Exp convolution left10 factorial step9 with exact rational arithmetic, not rounded decimals.
• S213 · premise_and_result_audit — Recompute Exp convolution left10 factorial step8 with exact rational arithmetic, not rounded decimals.
• S212 · premise_and_result_audit — Recompute Exp convolution left10 factorial step7 with exact rational arithmetic, not rounded decimals.
• S211 · premise_and_result_audit — Recompute Exp convolution left10 factorial step6 with exact rational arithmetic, not rounded decimals.
• S210 · premise_and_result_audit — Recompute Exp convolution left10 factorial step5 with exact rational arithmetic, not rounded decimals.
• S209 · premise_and_result_audit — Recompute Exp convolution left10 factorial step4 with exact rational arithmetic, not rounded decimals.
• S208 · premise_and_result_audit — Recompute Exp convolution left10 factorial step3 with exact rational arithmetic, not rounded decimals.
• S207 · premise_and_result_audit — Recompute Exp convolution left10 factorial step2 with exact rational arithmetic, not rounded decimals.
• S206 · premise_and_result_audit — Recompute Exp convolution left10 factorial step1 with exact rational arithmetic, not rounded decimals.
• S205 · premise_and_result_audit — Recompute Exp convolution numerator10 with exact rational arithmetic, not rounded decimals.
• S204 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S203 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S202 · premise_and_result_audit — Recompute Exp convolution coefficient term9 with exact rational arithmetic, not rounded decimals.
• S201 · premise_and_result_audit — Recompute Exp convolution denominator9 with exact rational arithmetic, not rounded decimals.
• S200 · premise_and_result_audit — Recompute Exp convolution right9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S199 · premise_and_result_audit — Recompute Exp convolution right9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S198 · premise_and_result_audit — Recompute Exp convolution right9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S197 · premise_and_result_audit — Recompute Exp convolution right9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S196 · premise_and_result_audit — Recompute Exp convolution right9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S195 · premise_and_result_audit — Recompute Exp convolution right9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S194 · premise_and_result_audit — Recompute Exp convolution left9 factorial step9 with exact rational arithmetic, not rounded decimals.
• S193 · premise_and_result_audit — Recompute Exp convolution left9 factorial step8 with exact rational arithmetic, not rounded decimals.
• S192 · premise_and_result_audit — Recompute Exp convolution left9 factorial step7 with exact rational arithmetic, not rounded decimals.
• S191 · premise_and_result_audit — Recompute Exp convolution left9 factorial step6 with exact rational arithmetic, not rounded decimals.
• S190 · premise_and_result_audit — Recompute Exp convolution left9 factorial step5 with exact rational arithmetic, not rounded decimals.
• S189 · premise_and_result_audit — Recompute Exp convolution left9 factorial step4 with exact rational arithmetic, not rounded decimals.
• S188 · premise_and_result_audit — Recompute Exp convolution left9 factorial step3 with exact rational arithmetic, not rounded decimals.
• S187 · premise_and_result_audit — Recompute Exp convolution left9 factorial step2 with exact rational arithmetic, not rounded decimals.
• S186 · premise_and_result_audit — Recompute Exp convolution left9 factorial step1 with exact rational arithmetic, not rounded decimals.
• S185 · premise_and_result_audit — Recompute Exp convolution numerator9 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 term8 with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Recompute Exp convolution denominator8 with exact rational arithmetic, not rounded decimals.
• S180 · premise_and_result_audit — Recompute Exp convolution right8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Recompute Exp convolution right8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S178 · premise_and_result_audit — Recompute Exp convolution right8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Recompute Exp convolution right8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S176 · premise_and_result_audit — Recompute Exp convolution right8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S175 · premise_and_result_audit — Recompute Exp convolution right8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S174 · premise_and_result_audit — Recompute Exp convolution right8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S173 · premise_and_result_audit — Recompute Exp convolution left8 factorial step8 with exact rational arithmetic, not rounded decimals.
• S172 · premise_and_result_audit — Recompute Exp convolution left8 factorial step7 with exact rational arithmetic, not rounded decimals.
• S171 · premise_and_result_audit — Recompute Exp convolution left8 factorial step6 with exact rational arithmetic, not rounded decimals.
• S170 · premise_and_result_audit — Recompute Exp convolution left8 factorial step5 with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Recompute Exp convolution left8 factorial step4 with exact rational arithmetic, not rounded decimals.
• S168 · premise_and_result_audit — Recompute Exp convolution left8 factorial step3 with exact rational arithmetic, not rounded decimals.
• S167 · premise_and_result_audit — Recompute Exp convolution left8 factorial step2 with exact rational arithmetic, not rounded decimals.
• S166 · premise_and_result_audit — Recompute Exp convolution left8 factorial step1 with exact rational arithmetic, not rounded decimals.
• S165 · premise_and_result_audit — Recompute Exp convolution numerator8 with exact rational arithmetic, not rounded decimals.
• S164 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S163 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S162 · premise_and_result_audit — Recompute Exp convolution coefficient term7 with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Recompute Exp convolution denominator7 with exact rational arithmetic, not rounded decimals.
• S160 · premise_and_result_audit — Recompute Exp convolution right7 factorial step8 with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Recompute Exp convolution right7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S158 · premise_and_result_audit — Recompute Exp convolution right7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Recompute Exp convolution right7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S156 · premise_and_result_audit — Recompute Exp convolution right7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S155 · premise_and_result_audit — Recompute Exp convolution right7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S154 · premise_and_result_audit — Recompute Exp convolution right7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S153 · premise_and_result_audit — Recompute Exp convolution right7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S152 · premise_and_result_audit — Recompute Exp convolution left7 factorial step7 with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Recompute Exp convolution left7 factorial step6 with exact rational arithmetic, not rounded decimals.
• S150 · premise_and_result_audit — Recompute Exp convolution left7 factorial step5 with exact rational arithmetic, not rounded decimals.
• S149 · premise_and_result_audit — Recompute Exp convolution left7 factorial step4 with exact rational arithmetic, not rounded decimals.
• S148 · premise_and_result_audit — Recompute Exp convolution left7 factorial step3 with exact rational arithmetic, not rounded decimals.
• S147 · premise_and_result_audit — Recompute Exp convolution left7 factorial step2 with exact rational arithmetic, not rounded decimals.
• S146 · premise_and_result_audit — Recompute Exp convolution left7 factorial step1 with exact rational arithmetic, not rounded decimals.
• S145 · premise_and_result_audit — Recompute Exp convolution numerator7 with exact rational arithmetic, not rounded decimals.
• S144 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S143 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S142 · premise_and_result_audit — Recompute Exp convolution coefficient term6 with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Recompute Exp convolution denominator6 with exact rational arithmetic, not rounded decimals.
• S140 · premise_and_result_audit — Recompute Exp convolution right6 factorial step9 with exact rational arithmetic, not rounded decimals.
• S139 · premise_and_result_audit — Recompute Exp convolution right6 factorial step8 with exact rational arithmetic, not rounded decimals.
• S138 · premise_and_result_audit — Recompute Exp convolution right6 factorial step7 with exact rational arithmetic, not rounded decimals.
• S137 · premise_and_result_audit — Recompute Exp convolution right6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S136 · premise_and_result_audit — Recompute Exp convolution right6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S135 · premise_and_result_audit — Recompute Exp convolution right6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S134 · premise_and_result_audit — Recompute Exp convolution right6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Recompute Exp convolution right6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S132 · premise_and_result_audit — Recompute Exp convolution right6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Recompute Exp convolution left6 factorial step6 with exact rational arithmetic, not rounded decimals.
• S130 · premise_and_result_audit — Recompute Exp convolution left6 factorial step5 with exact rational arithmetic, not rounded decimals.
• S129 · premise_and_result_audit — Recompute Exp convolution left6 factorial step4 with exact rational arithmetic, not rounded decimals.
• S128 · premise_and_result_audit — Recompute Exp convolution left6 factorial step3 with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Recompute Exp convolution left6 factorial step2 with exact rational arithmetic, not rounded decimals.
• S126 · premise_and_result_audit — Recompute Exp convolution left6 factorial step1 with exact rational arithmetic, not rounded decimals.
• S125 · premise_and_result_audit — Recompute Exp convolution numerator6 with exact rational arithmetic, not rounded decimals.
• S124 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S123 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S122 · premise_and_result_audit — Recompute Exp convolution coefficient term5 with exact rational arithmetic, not rounded decimals.
• S121 · premise_and_result_audit — Recompute Exp convolution denominator5 with exact rational arithmetic, not rounded decimals.
• S120 · premise_and_result_audit — Recompute Exp convolution right5 factorial step10 with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Recompute Exp convolution right5 factorial step9 with exact rational arithmetic, not rounded decimals.
• S118 · premise_and_result_audit — Recompute Exp convolution right5 factorial step8 with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Recompute Exp convolution right5 factorial step7 with exact rational arithmetic, not rounded decimals.
• S116 · premise_and_result_audit — Recompute Exp convolution right5 factorial step6 with exact rational arithmetic, not rounded decimals.
• S115 · premise_and_result_audit — Recompute Exp convolution right5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S114 · premise_and_result_audit — Recompute Exp convolution right5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Recompute Exp convolution right5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S112 · premise_and_result_audit — Recompute Exp convolution right5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S111 · premise_and_result_audit — Recompute Exp convolution right5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S110 · premise_and_result_audit — Recompute Exp convolution left5 factorial step5 with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Recompute Exp convolution left5 factorial step4 with exact rational arithmetic, not rounded decimals.
• S108 · premise_and_result_audit — Recompute Exp convolution left5 factorial step3 with exact rational arithmetic, not rounded decimals.
• S107 · premise_and_result_audit — Recompute Exp convolution left5 factorial step2 with exact rational arithmetic, not rounded decimals.
• S106 · premise_and_result_audit — Recompute Exp convolution left5 factorial step1 with exact rational arithmetic, not rounded decimals.
• S105 · premise_and_result_audit — Recompute Exp convolution numerator5 with exact rational arithmetic, not rounded decimals.
• S104 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S103 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S102 · premise_and_result_audit — Recompute Exp convolution coefficient term4 with exact rational arithmetic, not rounded decimals.
• S101 · premise_and_result_audit — Recompute Exp convolution denominator4 with exact rational arithmetic, not rounded decimals.
• S100 · premise_and_result_audit — Recompute Exp convolution right4 factorial step11 with exact rational arithmetic, not rounded decimals.
• S099 · premise_and_result_audit — Recompute Exp convolution right4 factorial step10 with exact rational arithmetic, not rounded decimals.
• S098 · premise_and_result_audit — Recompute Exp convolution right4 factorial step9 with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Recompute Exp convolution right4 factorial step8 with exact rational arithmetic, not rounded decimals.
• S096 · premise_and_result_audit — Recompute Exp convolution right4 factorial step7 with exact rational arithmetic, not rounded decimals.
• S095 · premise_and_result_audit — Recompute Exp convolution right4 factorial step6 with exact rational arithmetic, not rounded decimals.
• S094 · premise_and_result_audit — Recompute Exp convolution right4 factorial step5 with exact rational arithmetic, not rounded decimals.
• S093 · premise_and_result_audit — Recompute Exp convolution right4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S092 · premise_and_result_audit — Recompute Exp convolution right4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S091 · premise_and_result_audit — Recompute Exp convolution right4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S090 · premise_and_result_audit — Recompute Exp convolution right4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S089 · premise_and_result_audit — Recompute Exp convolution left4 factorial step4 with exact rational arithmetic, not rounded decimals.
• S088 · premise_and_result_audit — Recompute Exp convolution left4 factorial step3 with exact rational arithmetic, not rounded decimals.
• S087 · premise_and_result_audit — Recompute Exp convolution left4 factorial step2 with exact rational arithmetic, not rounded decimals.
• S086 · premise_and_result_audit — Recompute Exp convolution left4 factorial step1 with exact rational arithmetic, not rounded decimals.
• S085 · premise_and_result_audit — Recompute Exp convolution numerator4 with exact rational arithmetic, not rounded decimals.
• S084 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S083 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S082 · premise_and_result_audit — Recompute Exp convolution coefficient term3 with exact rational arithmetic, not rounded decimals.
• S081 · premise_and_result_audit — Recompute Exp convolution denominator3 with exact rational arithmetic, not rounded decimals.
• S080 · premise_and_result_audit — Recompute Exp convolution right3 factorial step12 with exact rational arithmetic, not rounded decimals.
• S079 · premise_and_result_audit — Recompute Exp convolution right3 factorial step11 with exact rational arithmetic, not rounded decimals.
• S078 · premise_and_result_audit — Recompute Exp convolution right3 factorial step10 with exact rational arithmetic, not rounded decimals.
• S077 · premise_and_result_audit — Recompute Exp convolution right3 factorial step9 with exact rational arithmetic, not rounded decimals.
• S076 · premise_and_result_audit — Recompute Exp convolution right3 factorial step8 with exact rational arithmetic, not rounded decimals.
• S075 · premise_and_result_audit — Recompute Exp convolution right3 factorial step7 with exact rational arithmetic, not rounded decimals.
• S074 · premise_and_result_audit — Recompute Exp convolution right3 factorial step6 with exact rational arithmetic, not rounded decimals.
• S073 · premise_and_result_audit — Recompute Exp convolution right3 factorial step5 with exact rational arithmetic, not rounded decimals.
• S072 · premise_and_result_audit — Recompute Exp convolution right3 factorial step4 with exact rational arithmetic, not rounded decimals.
• S071 · premise_and_result_audit — Recompute Exp convolution right3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S070 · premise_and_result_audit — Recompute Exp convolution right3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S069 · premise_and_result_audit — Recompute Exp convolution right3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S068 · premise_and_result_audit — Recompute Exp convolution left3 factorial step3 with exact rational arithmetic, not rounded decimals.
• S067 · premise_and_result_audit — Recompute Exp convolution left3 factorial step2 with exact rational arithmetic, not rounded decimals.
• S066 · premise_and_result_audit — Recompute Exp convolution left3 factorial step1 with exact rational arithmetic, not rounded decimals.
• S065 · premise_and_result_audit — Recompute Exp convolution numerator3 with exact rational arithmetic, not rounded decimals.
• S064 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S063 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S062 · premise_and_result_audit — Recompute Exp convolution coefficient term2 with exact rational arithmetic, not rounded decimals.
• S061 · premise_and_result_audit — Recompute Exp convolution denominator2 with exact rational arithmetic, not rounded decimals.
• S060 · premise_and_result_audit — Recompute Exp convolution right2 factorial step13 with exact rational arithmetic, not rounded decimals.
• S059 · premise_and_result_audit — Recompute Exp convolution right2 factorial step12 with exact rational arithmetic, not rounded decimals.
• S058 · premise_and_result_audit — Recompute Exp convolution right2 factorial step11 with exact rational arithmetic, not rounded decimals.
• S057 · premise_and_result_audit — Recompute Exp convolution right2 factorial step10 with exact rational arithmetic, not rounded decimals.
• S056 · premise_and_result_audit — Recompute Exp convolution right2 factorial step9 with exact rational arithmetic, not rounded decimals.
• S055 · premise_and_result_audit — Recompute Exp convolution right2 factorial step8 with exact rational arithmetic, not rounded decimals.
• S054 · premise_and_result_audit — Recompute Exp convolution right2 factorial step7 with exact rational arithmetic, not rounded decimals.
• S053 · premise_and_result_audit — Recompute Exp convolution right2 factorial step6 with exact rational arithmetic, not rounded decimals.
• S052 · premise_and_result_audit — Recompute Exp convolution right2 factorial step5 with exact rational arithmetic, not rounded decimals.
• S051 · premise_and_result_audit — Recompute Exp convolution right2 factorial step4 with exact rational arithmetic, not rounded decimals.
• S050 · premise_and_result_audit — Recompute Exp convolution right2 factorial step3 with exact rational arithmetic, not rounded decimals.
• S049 · premise_and_result_audit — Recompute Exp convolution right2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S048 · premise_and_result_audit — Recompute Exp convolution right2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S047 · premise_and_result_audit — Recompute Exp convolution left2 factorial step2 with exact rational arithmetic, not rounded decimals.
• S046 · premise_and_result_audit — Recompute Exp convolution left2 factorial step1 with exact rational arithmetic, not rounded decimals.
• S045 · premise_and_result_audit — Recompute Exp convolution numerator2 with exact rational arithmetic, not rounded decimals.
• S044 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S043 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S042 · premise_and_result_audit — Recompute Exp convolution coefficient term1 with exact rational arithmetic, not rounded decimals.
• S041 · premise_and_result_audit — Recompute Exp convolution denominator1 with exact rational arithmetic, not rounded decimals.
• S040 · premise_and_result_audit — Recompute Exp convolution right1 factorial step14 with exact rational arithmetic, not rounded decimals.
• S039 · premise_and_result_audit — Recompute Exp convolution right1 factorial step13 with exact rational arithmetic, not rounded decimals.
• S038 · premise_and_result_audit — Recompute Exp convolution right1 factorial step12 with exact rational arithmetic, not rounded decimals.
• S037 · premise_and_result_audit — Recompute Exp convolution right1 factorial step11 with exact rational arithmetic, not rounded decimals.
• S036 · premise_and_result_audit — Recompute Exp convolution right1 factorial step10 with exact rational arithmetic, not rounded decimals.
• S035 · premise_and_result_audit — Recompute Exp convolution right1 factorial step9 with exact rational arithmetic, not rounded decimals.
• S034 · premise_and_result_audit — Recompute Exp convolution right1 factorial step8 with exact rational arithmetic, not rounded decimals.
• S033 · premise_and_result_audit — Recompute Exp convolution right1 factorial step7 with exact rational arithmetic, not rounded decimals.
• S032 · premise_and_result_audit — Recompute Exp convolution right1 factorial step6 with exact rational arithmetic, not rounded decimals.
• S031 · premise_and_result_audit — Recompute Exp convolution right1 factorial step5 with exact rational arithmetic, not rounded decimals.
• S030 · premise_and_result_audit — Recompute Exp convolution right1 factorial step4 with exact rational arithmetic, not rounded decimals.
• S029 · premise_and_result_audit — Recompute Exp convolution right1 factorial step3 with exact rational arithmetic, not rounded decimals.
• S028 · premise_and_result_audit — Recompute Exp convolution right1 factorial step2 with exact rational arithmetic, not rounded decimals.
• S027 · premise_and_result_audit — Recompute Exp convolution right1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S026 · premise_and_result_audit — Recompute Exp convolution left1 factorial step1 with exact rational arithmetic, not rounded decimals.
• S025 · premise_and_result_audit — Recompute Exp convolution numerator1 with exact rational arithmetic, not rounded decimals.
• S024 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S023 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S022 · premise_and_result_audit — Recompute Exp convolution coefficient term0 with exact rational arithmetic, not rounded decimals.
• S021 · premise_and_result_audit — Recompute Exp convolution denominator0 with exact rational arithmetic, not rounded decimals.
• S020 · premise_and_result_audit — Recompute Exp convolution right0 factorial step15 with exact rational arithmetic, not rounded decimals.
• S019 · premise_and_result_audit — Recompute Exp convolution right0 factorial step14 with exact rational arithmetic, not rounded decimals.
• S018 · premise_and_result_audit — Recompute Exp convolution right0 factorial step13 with exact rational arithmetic, not rounded decimals.
• S017 · premise_and_result_audit — Recompute Exp convolution right0 factorial step12 with exact rational arithmetic, not rounded decimals.
• S016 · premise_and_result_audit — Recompute Exp convolution right0 factorial step11 with exact rational arithmetic, not rounded decimals.
• S015 · premise_and_result_audit — Recompute Exp convolution right0 factorial step10 with exact rational arithmetic, not rounded decimals.
• S014 · premise_and_result_audit — Recompute Exp convolution right0 factorial step9 with exact rational arithmetic, not rounded decimals.
• S013 · premise_and_result_audit — Recompute Exp convolution right0 factorial step8 with exact rational arithmetic, not rounded decimals.
• S012 · premise_and_result_audit — Recompute Exp convolution right0 factorial step7 with exact rational arithmetic, not rounded decimals.
• S011 · premise_and_result_audit — Recompute Exp convolution right0 factorial step6 with exact rational arithmetic, not rounded decimals.
• S010 · premise_and_result_audit — Recompute Exp convolution right0 factorial step5 with exact rational arithmetic, not rounded decimals.
• S009 · premise_and_result_audit — Recompute Exp convolution right0 factorial step4 with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute Exp convolution right0 factorial step3 with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute Exp convolution right0 factorial step2 with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Recompute Exp convolution right0 factorial step1 with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Recompute Exp convolution numerator0 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(16/17, -17/18, 15, [[0, -2862423051509815793/8822409004275290841311870976000], [1, 9904578032905937/2042224306545206213266636800], [2, -34271896307633/1013008088564090383564800], [3, 118587876497/811705199169944217600], [4, -410338673/939473610150398400], [5, 1419857/1482755066525250], [6, -78608/49425168884175], [7, 8704/4271310891225], [8, -16384/8068031683425], [9, 524288/333094450929975], [10, -16777216/17826721540511625], [11, 536870912/1259358839495254575], [12, -17179869184/121318234871376190725], [13, 549755813888/16881207718954086983475], [14, -17592186044416/3794520357271568663063325], [15, 562949953421312/1827693972085805572708834875]], -1/25253466903685353496585230352209316437943123968000, -1/25253466903685353496585230352209316437943123968000, 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.