第 24219 題：實指數函數

原題與已知條件

E(x)=sum_n>=0 x^n/n!的完整coefficient law與exact rational certificate。操作=exp-addition-convolution；資料={"x":[19,20],"y":[-20,21],"degree":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — E(x)=sum_n>=0 x^n/n!的完整coefficient law與exact rational certificate。操作=exp-addition-convolution；資料={"x":[19,20],"y":[-20,21],"degree":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-real-exponential-function

逐步推導

source roles = [exp-addition-convolution]

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

(19/20)^0

Exp convolution x power0 = 1

(-20/21)^18

Exp convolution y power18 = 262144000000000000000000/630880792396715529789561

Exp convolution numerator0 := mul(1, 262144000000000000000000/630880792396715529789561)

Exp convolution numerator0 = 262144000000000000000000/630880792396715529789561

source roles = [0]

derived = [1]

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

Exp convolution right0 factorial step1 = 1

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

Exp convolution right0 factorial step2 = 2

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

Exp convolution right0 factorial step3 = 6

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

Exp convolution right0 factorial step4 = 24

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

Exp convolution right0 factorial step5 = 120

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

Exp convolution right0 factorial step6 = 720

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

Exp convolution right0 factorial step7 = 5040

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

Exp convolution right0 factorial step8 = 40320

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

Exp convolution right0 factorial step9 = 362880

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

Exp convolution right0 factorial step10 = 3628800

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

Exp convolution right0 factorial step11 = 39916800

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

Exp convolution right0 factorial step12 = 479001600

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

Exp convolution right0 factorial step13 = 6227020800

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

Exp convolution right0 factorial step14 = 87178291200

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

Exp convolution right0 factorial step15 = 1307674368000

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

Exp convolution right0 factorial step16 = 20922789888000

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

Exp convolution right0 factorial step17 = 355687428096000

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

Exp convolution right0 factorial step18 = 6402373705728000

Exp convolution denominator0 := mul(1, 6402373705728000)

Exp convolution denominator0 = 6402373705728000

Exp convolution coefficient term0 := div(262144000000000000000000/630880792396715529789561, 6402373705728000)

Exp convolution coefficient term0 = 32000000000000000/493058422447458087543290824655799

(19/20)^1

Exp convolution x power1 = 19/20

(-20/21)^17

Exp convolution y power17 = -13107200000000000000000/30041942495081691894741

Exp convolution numerator1 := mul(19/20, -13107200000000000000000/30041942495081691894741)

Exp convolution numerator1 = -12451840000000000000000/30041942495081691894741

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

Exp convolution left1 factorial step1 = 1

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

Exp convolution right1 factorial step1 = 1

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

Exp convolution right1 factorial step2 = 2

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

Exp convolution right1 factorial step3 = 6

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

Exp convolution right1 factorial step4 = 24

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

Exp convolution right1 factorial step5 = 120

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

Exp convolution right1 factorial step6 = 720

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

Exp convolution right1 factorial step7 = 5040

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

Exp convolution right1 factorial step8 = 40320

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

Exp convolution right1 factorial step9 = 362880

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

Exp convolution right1 factorial step10 = 3628800

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

Exp convolution right1 factorial step11 = 39916800

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

Exp convolution right1 factorial step12 = 479001600

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

Exp convolution right1 factorial step13 = 6227020800

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

Exp convolution right1 factorial step14 = 87178291200

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

Exp convolution right1 factorial step15 = 1307674368000

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

Exp convolution right1 factorial step16 = 20922789888000

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

Exp convolution right1 factorial step17 = 355687428096000

Exp convolution denominator1 := mul(1, 355687428096000)

Exp convolution denominator1 = 355687428096000

Exp convolution coefficient term1 := div(-12451840000000000000000/30041942495081691894741, 355687428096000)

Exp convolution coefficient term1 = -3040000000000000/2608774721944222685414237167491

(19/20)^2

Exp convolution x power2 = 361/400

(-20/21)^16

Exp convolution y power16 = 655360000000000000000/1430568690241985328321

Exp convolution numerator2 := mul(361/400, 655360000000000000000/1430568690241985328321)

Exp convolution numerator2 = 591462400000000000000/1430568690241985328321

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

Exp convolution left2 factorial step1 = 1

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

Exp convolution left2 factorial step2 = 2

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

Exp convolution right2 factorial step1 = 1

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

Exp convolution right2 factorial step2 = 2

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

Exp convolution right2 factorial step3 = 6

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

Exp convolution right2 factorial step4 = 24

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

Exp convolution right2 factorial step5 = 120

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

Exp convolution right2 factorial step6 = 720

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

Exp convolution right2 factorial step7 = 5040

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

Exp convolution right2 factorial step8 = 40320

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

Exp convolution right2 factorial step9 = 362880

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

Exp convolution right2 factorial step10 = 3628800

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

Exp convolution right2 factorial step11 = 39916800

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

Exp convolution right2 factorial step12 = 479001600

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

Exp convolution right2 factorial step13 = 6227020800

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

Exp convolution right2 factorial step14 = 87178291200

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

Exp convolution right2 factorial step15 = 1307674368000

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

Exp convolution right2 factorial step16 = 20922789888000

Exp convolution denominator2 := mul(2, 20922789888000)

Exp convolution denominator2 = 41845579776000

Exp convolution coefficient term2 := div(591462400000000000000/1430568690241985328321, 41845579776000)

Exp convolution coefficient term2 = 72200000000000/7307492218331155981552485063

(19/20)^3

Exp convolution x power3 = 6859/8000

(-20/21)^15

Exp convolution y power15 = -32768000000000000000/68122318582951682301

Exp convolution numerator3 := mul(6859/8000, -32768000000000000000/68122318582951682301)

Exp convolution numerator3 = -28094464000000000000/68122318582951682301

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

Exp convolution left3 factorial step1 = 1

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

Exp convolution left3 factorial step2 = 2

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

Exp convolution left3 factorial step3 = 6

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

Exp convolution right3 factorial step1 = 1

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

Exp convolution right3 factorial step2 = 2

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

Exp convolution right3 factorial step3 = 6

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

Exp convolution right3 factorial step4 = 24

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

Exp convolution right3 factorial step5 = 120

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

Exp convolution right3 factorial step6 = 720

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

Exp convolution right3 factorial step7 = 5040

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

Exp convolution right3 factorial step8 = 40320

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

Exp convolution right3 factorial step9 = 362880

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

Exp convolution right3 factorial step10 = 3628800

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

Exp convolution right3 factorial step11 = 39916800

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

Exp convolution right3 factorial step12 = 479001600

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

Exp convolution right3 factorial step13 = 6227020800

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

Exp convolution right3 factorial step14 = 87178291200

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

Exp convolution right3 factorial step15 = 1307674368000

Exp convolution denominator3 := mul(6, 1307674368000)

Exp convolution denominator3 = 7846046208000

Exp convolution coefficient term3 := div(-28094464000000000000/68122318582951682301, 7846046208000)

Exp convolution coefficient term3 = -54872000000000/1043927459761593711650355009

(19/20)^4

Exp convolution x power4 = 130321/160000

(-20/21)^14

Exp convolution y power14 = 1638400000000000000/3243919932521508681

Exp convolution numerator4 := mul(130321/160000, 1638400000000000000/3243919932521508681)

Exp convolution numerator4 = 1334487040000000000/3243919932521508681

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

Exp convolution left4 factorial step1 = 1

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

Exp convolution left4 factorial step2 = 2

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

Exp convolution left4 factorial step3 = 6

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

Exp convolution left4 factorial step4 = 24

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

Exp convolution right4 factorial step1 = 1

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

Exp convolution right4 factorial step2 = 2

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

Exp convolution right4 factorial step3 = 6

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

Exp convolution right4 factorial step4 = 24

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

Exp convolution right4 factorial step5 = 120

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

Exp convolution right4 factorial step6 = 720

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

Exp convolution right4 factorial step7 = 5040

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

Exp convolution right4 factorial step8 = 40320

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

Exp convolution right4 factorial step9 = 362880

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

Exp convolution right4 factorial step10 = 3628800

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

Exp convolution right4 factorial step11 = 39916800

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

Exp convolution right4 factorial step12 = 479001600

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

Exp convolution right4 factorial step13 = 6227020800

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

Exp convolution right4 factorial step14 = 87178291200

Exp convolution denominator4 := mul(24, 87178291200)

Exp convolution denominator4 = 2092278988800

Exp convolution coefficient term4 := div(1334487040000000000/3243919932521508681, 2092278988800)

Exp convolution coefficient term4 = 3258025000000/16570277139072916057942143

(19/20)^5

Exp convolution x power5 = 2476099/3200000

(-20/21)^13

Exp convolution y power13 = -81920000000000000/154472377739119461

Exp convolution numerator5 := mul(2476099/3200000, -81920000000000000/154472377739119461)

Exp convolution numerator5 = -63388134400000000/154472377739119461

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

Exp convolution left5 factorial step1 = 1

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

Exp convolution left5 factorial step2 = 2

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

Exp convolution left5 factorial step3 = 6

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

Exp convolution left5 factorial step4 = 24

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

Exp convolution left5 factorial step5 = 120

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

Exp convolution right5 factorial step1 = 1

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

Exp convolution right5 factorial step2 = 2

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

Exp convolution right5 factorial step3 = 6

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

Exp convolution right5 factorial step4 = 24

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

Exp convolution right5 factorial step5 = 120

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

Exp convolution right5 factorial step6 = 720

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

Exp convolution right5 factorial step7 = 5040

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

Exp convolution right5 factorial step8 = 40320

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

Exp convolution right5 factorial step9 = 362880

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

Exp convolution right5 factorial step10 = 3628800

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

Exp convolution right5 factorial step11 = 39916800

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

Exp convolution right5 factorial step12 = 479001600

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

Exp convolution right5 factorial step13 = 6227020800

Exp convolution denominator5 := mul(120, 6227020800)

Exp convolution denominator5 = 747242496000

Exp convolution coefficient term5 := div(-63388134400000000/154472377739119461, 747242496000)

Exp convolution coefficient term5 = -61902475000/112722973735189905156069

(19/20)^6

Exp convolution x power6 = 47045881/64000000

(-20/21)^12

Exp convolution y power12 = 4096000000000000/7355827511386641

Exp convolution numerator6 := mul(47045881/64000000, 4096000000000000/7355827511386641)

Exp convolution numerator6 = 3010936384000000/7355827511386641

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

Exp convolution left6 factorial step1 = 1

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

Exp convolution left6 factorial step2 = 2

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

Exp convolution left6 factorial step3 = 6

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

Exp convolution left6 factorial step4 = 24

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

Exp convolution left6 factorial step5 = 120

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

Exp convolution left6 factorial step6 = 720

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

Exp convolution right6 factorial step1 = 1

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

Exp convolution right6 factorial step2 = 2

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

Exp convolution right6 factorial step3 = 6

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

Exp convolution right6 factorial step4 = 24

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

Exp convolution right6 factorial step5 = 120

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

Exp convolution right6 factorial step6 = 720

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

Exp convolution right6 factorial step7 = 5040

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

Exp convolution right6 factorial step8 = 40320

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

Exp convolution right6 factorial step9 = 362880

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

Exp convolution right6 factorial step10 = 3628800

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

Exp convolution right6 factorial step11 = 39916800

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

Exp convolution right6 factorial step12 = 479001600

Exp convolution denominator6 := mul(720, 479001600)

Exp convolution denominator6 = 344881152000

Exp convolution coefficient term6 := div(3010936384000000/7355827511386641, 344881152000)

Exp convolution coefficient term6 = 5880735125/4954855988359995831036

(19/20)^7

Exp convolution x power7 = 893871739/1280000000

(-20/21)^11

Exp convolution y power11 = -204800000000000/350277500542221

Exp convolution numerator7 := mul(893871739/1280000000, -204800000000000/350277500542221)

Exp convolution numerator7 = -143019478240000/350277500542221

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

Exp convolution left7 factorial step1 = 1

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

Exp convolution left7 factorial step2 = 2

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

Exp convolution left7 factorial step3 = 6

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

Exp convolution left7 factorial step4 = 24

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

Exp convolution left7 factorial step5 = 120

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

Exp convolution left7 factorial step6 = 720

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

Exp convolution left7 factorial step7 = 5040

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

Exp convolution right7 factorial step1 = 1

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

Exp convolution right7 factorial step2 = 2

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

Exp convolution right7 factorial step3 = 6

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

Exp convolution right7 factorial step4 = 24

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

Exp convolution right7 factorial step5 = 120

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

Exp convolution right7 factorial step6 = 720

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

Exp convolution right7 factorial step7 = 5040

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

Exp convolution right7 factorial step8 = 40320

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

Exp convolution right7 factorial step9 = 362880

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

Exp convolution right7 factorial step10 = 3628800

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

Exp convolution right7 factorial step11 = 39916800

Exp convolution denominator7 := mul(5040, 39916800)

Exp convolution denominator7 = 201180672000

Exp convolution coefficient term7 := div(-143019478240000/350277500542221, 201180672000)

Exp convolution coefficient term7 = -4469358695/2202158217048887036016

(19/20)^8

Exp convolution x power8 = 16983563041/25600000000

(-20/21)^10

Exp convolution y power10 = 10240000000000/16679880978201

Exp convolution numerator8 := mul(16983563041/25600000000, 10240000000000/16679880978201)

Exp convolution numerator8 = 6793425216400/16679880978201

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

Exp convolution left8 factorial step1 = 1

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

Exp convolution left8 factorial step2 = 2

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

Exp convolution left8 factorial step3 = 6

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

Exp convolution left8 factorial step4 = 24

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

Exp convolution left8 factorial step5 = 120

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

Exp convolution left8 factorial step6 = 720

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

Exp convolution left8 factorial step7 = 5040

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

Exp convolution left8 factorial step8 = 40320

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

Exp convolution right8 factorial step1 = 1

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

Exp convolution right8 factorial step2 = 2

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

Exp convolution right8 factorial step3 = 6

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

Exp convolution right8 factorial step4 = 24

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

Exp convolution right8 factorial step5 = 120

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

Exp convolution right8 factorial step6 = 720

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

Exp convolution right8 factorial step7 = 5040

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

Exp convolution right8 factorial step8 = 40320

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

Exp convolution right8 factorial step9 = 362880

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

Exp convolution right8 factorial step10 = 3628800

Exp convolution denominator8 := mul(40320, 3628800)

Exp convolution denominator8 = 146313216000

Exp convolution coefficient term8 := div(6793425216400/16679880978201, 146313216000)

Exp convolution coefficient term8 = 16983563041/6101217571044535511040

(19/20)^9

Exp convolution x power9 = 322687697779/512000000000

(-20/21)^9

Exp convolution y power9 = -512000000000/794280046581

Exp convolution numerator9 := mul(322687697779/512000000000, -512000000000/794280046581)

Exp convolution numerator9 = -322687697779/794280046581

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

Exp convolution left9 factorial step1 = 1

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

Exp convolution left9 factorial step2 = 2

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

Exp convolution left9 factorial step3 = 6

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

Exp convolution left9 factorial step4 = 24

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

Exp convolution left9 factorial step5 = 120

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

Exp convolution left9 factorial step6 = 720

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

Exp convolution left9 factorial step7 = 5040

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

Exp convolution left9 factorial step8 = 40320

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

Exp convolution left9 factorial step9 = 362880

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

Exp convolution right9 factorial step1 = 1

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

Exp convolution right9 factorial step2 = 2

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

Exp convolution right9 factorial step3 = 6

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

Exp convolution right9 factorial step4 = 24

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

Exp convolution right9 factorial step5 = 120

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

Exp convolution right9 factorial step6 = 720

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

Exp convolution right9 factorial step7 = 5040

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

Exp convolution right9 factorial step8 = 40320

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

Exp convolution right9 factorial step9 = 362880

Exp convolution denominator9 := mul(362880, 362880)

Exp convolution denominator9 = 131681894400

Exp convolution coefficient term9 := div(-322687697779/794280046581, 131681894400)

Exp convolution coefficient term9 = -322687697779/104592301217906323046400

(19/20)^10

Exp convolution x power10 = 6131066257801/10240000000000

(-20/21)^8

Exp convolution y power8 = 25600000000/37822859361

Exp convolution numerator10 := mul(6131066257801/10240000000000, 25600000000/37822859361)

Exp convolution numerator10 = 6131066257801/15129143744400

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

Exp convolution left10 factorial step1 = 1

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

Exp convolution left10 factorial step2 = 2

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

Exp convolution left10 factorial step3 = 6

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

Exp convolution left10 factorial step4 = 24

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

Exp convolution left10 factorial step5 = 120

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

Exp convolution left10 factorial step6 = 720

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

Exp convolution left10 factorial step7 = 5040

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

Exp convolution left10 factorial step8 = 40320

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

Exp convolution left10 factorial step9 = 362880

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

Exp convolution left10 factorial step10 = 3628800

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

Exp convolution right10 factorial step1 = 1

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

Exp convolution right10 factorial step2 = 2

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

Exp convolution right10 factorial step3 = 6

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

Exp convolution right10 factorial step4 = 24

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

Exp convolution right10 factorial step5 = 120

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

Exp convolution right10 factorial step6 = 720

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

Exp convolution right10 factorial step7 = 5040

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

Exp convolution right10 factorial step8 = 40320

Exp convolution denominator10 := mul(3628800, 40320)

Exp convolution denominator10 = 146313216000

Exp convolution coefficient term10 := div(6131066257801/15129143744400, 146313216000)

Exp convolution coefficient term10 = 6131066257801/2213593676569445990400000

(19/20)^11

Exp convolution x power11 = 116490258898219/204800000000000

(-20/21)^7

Exp convolution y power7 = -1280000000/1801088541

Exp convolution numerator11 := mul(116490258898219/204800000000000, -1280000000/1801088541)

Exp convolution numerator11 = -116490258898219/288174166560000

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

Exp convolution left11 factorial step1 = 1

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

Exp convolution left11 factorial step2 = 2

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

Exp convolution left11 factorial step3 = 6

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

Exp convolution left11 factorial step4 = 24

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

Exp convolution left11 factorial step5 = 120

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

Exp convolution left11 factorial step6 = 720

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

Exp convolution left11 factorial step7 = 5040

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

Exp convolution left11 factorial step8 = 40320

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

Exp convolution left11 factorial step9 = 362880

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

Exp convolution left11 factorial step10 = 3628800

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

Exp convolution left11 factorial step11 = 39916800

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

Exp convolution right11 factorial step1 = 1

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

Exp convolution right11 factorial step2 = 2

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

Exp convolution right11 factorial step3 = 6

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

Exp convolution right11 factorial step4 = 24

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

Exp convolution right11 factorial step5 = 120

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

Exp convolution right11 factorial step6 = 720

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

Exp convolution right11 factorial step7 = 5040

Exp convolution denominator11 := mul(39916800, 5040)

Exp convolution denominator11 = 201180672000

Exp convolution coefficient term11 := div(-116490258898219/288174166560000, 201180672000)

Exp convolution coefficient term11 = -116490258898219/57975072481580728320000000

(19/20)^12

Exp convolution x power12 = 2213314919066161/4096000000000000

(-20/21)^6

Exp convolution y power6 = 64000000/85766121

Exp convolution numerator12 := mul(2213314919066161/4096000000000000, 64000000/85766121)

Exp convolution numerator12 = 2213314919066161/5489031744000000

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

Exp convolution left12 factorial step1 = 1

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

Exp convolution left12 factorial step2 = 2

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

Exp convolution left12 factorial step3 = 6

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

Exp convolution left12 factorial step4 = 24

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

Exp convolution left12 factorial step5 = 120

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

Exp convolution left12 factorial step6 = 720

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

Exp convolution left12 factorial step7 = 5040

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

Exp convolution left12 factorial step8 = 40320

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

Exp convolution left12 factorial step9 = 362880

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

Exp convolution left12 factorial step10 = 3628800

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

Exp convolution left12 factorial step11 = 39916800

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

Exp convolution left12 factorial step12 = 479001600

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

Exp convolution right12 factorial step1 = 1

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

Exp convolution right12 factorial step2 = 2

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

Exp convolution right12 factorial step3 = 6

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

Exp convolution right12 factorial step4 = 24

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

Exp convolution right12 factorial step5 = 120

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

Exp convolution right12 factorial step6 = 720

Exp convolution denominator12 := mul(479001600, 720)

Exp convolution denominator12 = 344881152000

Exp convolution coefficient term12 := div(2213314919066161/5489031744000000, 344881152000)

Exp convolution coefficient term12 = 2213314919066161/1893063591235289088000000000

(19/20)^13

Exp convolution x power13 = 42052983462257059/81920000000000000

(-20/21)^5

Exp convolution y power5 = -3200000/4084101

Exp convolution numerator13 := mul(42052983462257059/81920000000000000, -3200000/4084101)

Exp convolution numerator13 = -42052983462257059/104552985600000000

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

Exp convolution left13 factorial step1 = 1

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

Exp convolution left13 factorial step2 = 2

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

Exp convolution left13 factorial step3 = 6

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

Exp convolution left13 factorial step4 = 24

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

Exp convolution left13 factorial step5 = 120

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

Exp convolution left13 factorial step6 = 720

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

Exp convolution left13 factorial step7 = 5040

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

Exp convolution left13 factorial step8 = 40320

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

Exp convolution left13 factorial step9 = 362880

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

Exp convolution left13 factorial step10 = 3628800

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

Exp convolution left13 factorial step11 = 39916800

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

Exp convolution left13 factorial step12 = 479001600

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

Exp convolution left13 factorial step13 = 6227020800

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

Exp convolution right13 factorial step1 = 1

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

Exp convolution right13 factorial step2 = 2

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

Exp convolution right13 factorial step3 = 6

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

Exp convolution right13 factorial step4 = 24

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

Exp convolution right13 factorial step5 = 120

Exp convolution denominator13 := mul(6227020800, 120)

Exp convolution denominator13 = 747242496000

Exp convolution coefficient term13 := div(-42052983462257059/104552985600000000, 747242496000)

Exp convolution coefficient term13 = -42052983462257059/78126433923996057600000000000

(19/20)^14

Exp convolution x power14 = 799006685782884121/1638400000000000000

(-20/21)^4

Exp convolution y power4 = 160000/194481

Exp convolution numerator14 := mul(799006685782884121/1638400000000000000, 160000/194481)

Exp convolution numerator14 = 799006685782884121/1991485440000000000

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

Exp convolution left14 factorial step1 = 1

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

Exp convolution left14 factorial step2 = 2

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

Exp convolution left14 factorial step3 = 6

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

Exp convolution left14 factorial step4 = 24

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

Exp convolution left14 factorial step5 = 120

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

Exp convolution left14 factorial step6 = 720

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

Exp convolution left14 factorial step7 = 5040

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

Exp convolution left14 factorial step8 = 40320

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

Exp convolution left14 factorial step9 = 362880

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

Exp convolution left14 factorial step10 = 3628800

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

Exp convolution left14 factorial step11 = 39916800

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

Exp convolution left14 factorial step12 = 479001600

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

Exp convolution left14 factorial step13 = 6227020800

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

Exp convolution left14 factorial step14 = 87178291200

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

Exp convolution right14 factorial step1 = 1

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

Exp convolution right14 factorial step2 = 2

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

Exp convolution right14 factorial step3 = 6

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

Exp convolution right14 factorial step4 = 24

Exp convolution denominator14 := mul(87178291200, 24)

Exp convolution denominator14 = 2092278988800

Exp convolution coefficient term14 := div(799006685782884121/1991485440000000000, 2092278988800)

Exp convolution coefficient term14 = 799006685782884121/4166743142613123072000000000000

(19/20)^15

Exp convolution x power15 = 15181127029874798299/32768000000000000000

(-20/21)^3

Exp convolution y power3 = -8000/9261

Exp convolution numerator15 := mul(15181127029874798299/32768000000000000000, -8000/9261)

Exp convolution numerator15 = -15181127029874798299/37933056000000000000

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

Exp convolution left15 factorial step1 = 1

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

Exp convolution left15 factorial step2 = 2

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

Exp convolution left15 factorial step3 = 6

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

Exp convolution left15 factorial step4 = 24

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

Exp convolution left15 factorial step5 = 120

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

Exp convolution left15 factorial step6 = 720

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

Exp convolution left15 factorial step7 = 5040

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

Exp convolution left15 factorial step8 = 40320

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

Exp convolution left15 factorial step9 = 362880

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

Exp convolution left15 factorial step10 = 3628800

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

Exp convolution left15 factorial step11 = 39916800

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

Exp convolution left15 factorial step12 = 479001600

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

Exp convolution left15 factorial step13 = 6227020800

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

Exp convolution left15 factorial step14 = 87178291200

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

Exp convolution left15 factorial step15 = 1307674368000

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

Exp convolution right15 factorial step1 = 1

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

Exp convolution right15 factorial step2 = 2

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

Exp convolution right15 factorial step3 = 6

Exp convolution denominator15 := mul(1307674368000, 6)

Exp convolution denominator15 = 7846046208000

Exp convolution coefficient term15 := div(-15181127029874798299/37933056000000000000, 7846046208000)

Exp convolution coefficient term15 = -15181127029874798299/297624510186651648000000000000000

(19/20)^16

Exp convolution x power16 = 288441413567621167681/655360000000000000000

(-20/21)^2

Exp convolution y power2 = 400/441

Exp convolution numerator16 := mul(288441413567621167681/655360000000000000000, 400/441)

Exp convolution numerator16 = 288441413567621167681/722534400000000000000

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

Exp convolution left16 factorial step1 = 1

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

Exp convolution left16 factorial step2 = 2

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

Exp convolution left16 factorial step3 = 6

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

Exp convolution left16 factorial step4 = 24

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

Exp convolution left16 factorial step5 = 120

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

Exp convolution left16 factorial step6 = 720

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

Exp convolution left16 factorial step7 = 5040

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

Exp convolution left16 factorial step8 = 40320

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

Exp convolution left16 factorial step9 = 362880

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

Exp convolution left16 factorial step10 = 3628800

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

Exp convolution left16 factorial step11 = 39916800

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

Exp convolution left16 factorial step12 = 479001600

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

Exp convolution left16 factorial step13 = 6227020800

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

Exp convolution left16 factorial step14 = 87178291200

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

Exp convolution left16 factorial step15 = 1307674368000

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

Exp convolution left16 factorial step16 = 20922789888000

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

Exp convolution right16 factorial step1 = 1

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

Exp convolution right16 factorial step2 = 2

Exp convolution denominator16 := mul(20922789888000, 2)

Exp convolution denominator16 = 41845579776000

Exp convolution coefficient term16 := div(288441413567621167681/722534400000000000000, 41845579776000)

Exp convolution coefficient term16 = 288441413567621167681/30234870876104294400000000000000000

(19/20)^17

Exp convolution x power17 = 5480386857784802185939/13107200000000000000000

(-20/21)^1

Exp convolution y power1 = -20/21

Exp convolution numerator17 := mul(5480386857784802185939/13107200000000000000000, -20/21)

Exp convolution numerator17 = -5480386857784802185939/13762560000000000000000

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

Exp convolution left17 factorial step1 = 1

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

Exp convolution left17 factorial step2 = 2

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

Exp convolution left17 factorial step3 = 6

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

Exp convolution left17 factorial step4 = 24

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

Exp convolution left17 factorial step5 = 120

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

Exp convolution left17 factorial step6 = 720

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

Exp convolution left17 factorial step7 = 5040

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

Exp convolution left17 factorial step8 = 40320

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

Exp convolution left17 factorial step9 = 362880

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

Exp convolution left17 factorial step10 = 3628800

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

Exp convolution left17 factorial step11 = 39916800

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

Exp convolution left17 factorial step12 = 479001600

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

Exp convolution left17 factorial step13 = 6227020800

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

Exp convolution left17 factorial step14 = 87178291200

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

Exp convolution left17 factorial step15 = 1307674368000

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

Exp convolution left17 factorial step16 = 20922789888000

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

Exp convolution left17 factorial step17 = 355687428096000

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

Exp convolution right17 factorial step1 = 1

Exp convolution denominator17 := mul(355687428096000, 1)

Exp convolution denominator17 = 355687428096000

Exp convolution coefficient term17 := div(-5480386857784802185939/13762560000000000000000, 355687428096000)

Exp convolution coefficient term17 = -5480386857784802185939/4895169570416885760000000000000000000

(19/20)^18

Exp convolution x power18 = 104127350297911241532841/262144000000000000000000

(-20/21)^0

Exp convolution y power0 = 1

Exp convolution numerator18 := mul(104127350297911241532841/262144000000000000000000, 1)

Exp convolution numerator18 = 104127350297911241532841/262144000000000000000000

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

Exp convolution left18 factorial step1 = 1

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

Exp convolution left18 factorial step2 = 2

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

Exp convolution left18 factorial step3 = 6

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

Exp convolution left18 factorial step4 = 24

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

Exp convolution left18 factorial step5 = 120

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

Exp convolution left18 factorial step6 = 720

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

Exp convolution left18 factorial step7 = 5040

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

Exp convolution left18 factorial step8 = 40320

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

Exp convolution left18 factorial step9 = 362880

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

Exp convolution left18 factorial step10 = 3628800

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

Exp convolution left18 factorial step11 = 39916800

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

Exp convolution left18 factorial step12 = 479001600

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

Exp convolution left18 factorial step13 = 6227020800

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

Exp convolution left18 factorial step14 = 87178291200

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

Exp convolution left18 factorial step15 = 1307674368000

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

Exp convolution left18 factorial step16 = 20922789888000

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

Exp convolution left18 factorial step17 = 355687428096000

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

Exp convolution left18 factorial step18 = 6402373705728000

source roles = [0]

derived = [1]

Exp convolution denominator18 := mul(6402373705728000, 1)

Exp convolution denominator18 = 6402373705728000

Exp convolution coefficient term18 := div(104127350297911241532841/262144000000000000000000, 6402373705728000)

Exp convolution coefficient term18 = 104127350297911241532841/1678343852714360832000000000000000000000

Exp complete declared-degree convolution := sum(32000000000000000/493058422447458087543290824655799, -3040000000000000/2608774721944222685414237167491, 72200000000000/7307492218331155981552485063, -54872000000000/1043927459761593711650355009, 3258025000000/16570277139072916057942143, -61902475000/112722973735189905156069, 5880735125/4954855988359995831036, -4469358695/2202158217048887036016, 16983563041/6101217571044535511040, -322687697779/104592301217906323046400, 6131066257801/2213593676569445990400000, -116490258898219/57975072481580728320000000, 2213314919066161/1893063591235289088000000000, -42052983462257059/78126433923996057600000000000, 799006685782884121/4166743142613123072000000000000, -15181127029874798299/297624510186651648000000000000000, 288441413567621167681/30234870876104294400000000000000000, -5480386857784802185939/4895169570416885760000000000000000000, 104127350297911241532841/1678343852714360832000000000000000000000)

Exp complete declared-degree convolution = 1/1058834899714592382164569538056763580874752000000000000000000000

Exp ORIGINAL arguments sum := sum(19/20, -20/21)

Exp ORIGINAL arguments sum = -1/420

(-1/420)^18

Exp sum argument declared power = 1/165381614442044595841154678784000000000000000000

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

Exp sum argument factorial step1 = 1

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

Exp sum argument factorial step2 = 2

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

Exp sum argument factorial step3 = 6

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

Exp sum argument factorial step4 = 24

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

Exp sum argument factorial step5 = 120

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

Exp sum argument factorial step6 = 720

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

Exp sum argument factorial step7 = 5040

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

Exp sum argument factorial step8 = 40320

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

Exp sum argument factorial step9 = 362880

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

Exp sum argument factorial step10 = 3628800

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

Exp sum argument factorial step11 = 39916800

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

Exp sum argument factorial step12 = 479001600

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

Exp sum argument factorial step13 = 6227020800

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

Exp sum argument factorial step14 = 87178291200

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

Exp sum argument factorial step15 = 1307674368000

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

Exp sum argument factorial step16 = 20922789888000

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

Exp sum argument factorial step17 = 355687428096000

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

Exp sum argument factorial step18 = 6402373705728000

Exp sum argument coefficient := div(1/165381614442044595841154678784000000000000000000, 6402373705728000)

Exp sum argument coefficient = 1/1058834899714592382164569538056763580874752000000000000000000000

source roles = [[19/20, -20/21], 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 = [[19/20, -20/21, 18], 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)]

逐步反向核對

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

結論

(19/20, -20/21, 18, [[0, 32000000000000000/493058422447458087543290824655799], [1, -3040000000000000/2608774721944222685414237167491], [2, 72200000000000/7307492218331155981552485063], [3, -54872000000000/1043927459761593711650355009], [4, 3258025000000/16570277139072916057942143], [5, -61902475000/112722973735189905156069], [6, 5880735125/4954855988359995831036], [7, -4469358695/2202158217048887036016], [8, 16983563041/6101217571044535511040], [9, -322687697779/104592301217906323046400], [10, 6131066257801/2213593676569445990400000], [11, -116490258898219/57975072481580728320000000], [12, 2213314919066161/1893063591235289088000000000], [13, -42052983462257059/78126433923996057600000000000], [14, 799006685782884121/4166743142613123072000000000000], [15, -15181127029874798299/297624510186651648000000000000000], [16, 288441413567621167681/30234870876104294400000000000000000], [17, -5480386857784802185939/4895169570416885760000000000000000000], [18, 104127350297911241532841/1678343852714360832000000000000000000000]], 1/1058834899714592382164569538056763580874752000000000000000000000, 1/1058834899714592382164569538056763580874752000000000000000000000, 是, binomial_convolution_matches_the_declared_degree;the_general_addition_law_requires_all_degrees_plus_absolute_convergence_for_Cauchy_product_rearrangement)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。