mirror of
https://github.com/opelly27/Y-Cruncher.git
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opelly27
259 lines
10 KiB
INI
259 lines
10 KiB
INI
// y-cruncher Custom Formula File
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//
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// This can be loaded directly from the Custom Compute menu or
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// entered from the command line as "custom:filename.cfg".
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// y-cruncher custom custom:"filename.cfg"
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//
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//
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// Author: Alexander J. Yee
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// Date: October 2, 2018
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//
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// Value = 1.03692775514336992633136548645703416805708091950191...
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//
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// Formula: Broadhurst (1998)
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// https://arxiv.org/pdf/math/9803067.pdf
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//
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// 1152 inf 1 ( 248 12912 124 24848 62 3228 31 74552 )
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// Zeta(5) = ------- SUM ------ (---------- - ---------- - ---------- - ---------- - ---------- - ---------- + ---------- + ----------)
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// 62651 k=0 16^k ( (8k+1)^5 (8k+2)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+6)^5 (8k+7)^5 (8k+8)^5 )
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//
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// 7 inf 1 ( 177152 145408 22144 29248 2768 2272 346 111 )
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// + -------- SUM -------- (---------- + ---------- - ---------- - ---------- - ---------- + ---------- + ---------- - ----------)
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// 250604 k=0 4096^k ( (8k+1)^5 (8k+2)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+6)^5 (8k+7)^5 (8k+8)^5 )
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//
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// 369 inf 1 ( 131072 4096 1024 128 4 1 )
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// + ---------- SUM --------- (- ---------- + ---------- + ---------- + ---------- - ---------- - ----------)
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// 64154624 k=0 2^(20k) ( (8k+1)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+7)^5 (8k+8)^5 )
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//
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{
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NameShort : "Zeta(5)"
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NameLong : "Zeta(5)"
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AlgorithmShort : "Broadhurst"
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AlgorithmLong : "Broadhurst (1998)"
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Formula : {
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LinearCombination : [
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 14
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PolynomialP : [9]
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PolynomialQ : [-16807 96040 -219520 250880 -143360 32768]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 13
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PolynomialP : [9]
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PolynomialQ : [-3125 25000 -80000 128000 -102400 32768]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 12
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PolynomialP : [9]
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PolynomialQ : [-243 3240 -17280 46080 -61440 32768]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2021
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 11
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PolynomialP : [9]
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PolynomialQ : [-1 40 -640 5120 -20480 32768]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 10
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PolynomialP : [7263]
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PolynomialQ : [-243 1620 -4320 5760 -3840 1024]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 8
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PolynomialP : [7263]
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PolynomialQ : [-1 20 -160 640 -1280 1024]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 5
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PolynomialP : [13977]
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PolynomialQ : [-1 10 -40 80 -80 32]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 125302
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Alternating : "false"
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PowerCoef : -4
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PowerShift : 0
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PolynomialP : [83871]
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PolynomialQ : [0 0 0 0 0 1]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 20
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PolynomialP : [1211]
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PolynomialQ : [-16807 96040 -219520 250880 -143360 32768]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 17
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PolynomialP : [1211]
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PolynomialQ : [-3125 25000 -80000 128000 -102400 32768]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 14
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PolynomialP : [1211]
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PolynomialQ : [-243 3240 -17280 46080 -61440 32768]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 11
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PolynomialP : [1211]
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PolynomialQ : [-1 40 -640 5120 -20480 32768]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 16
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PolynomialP : [497]
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PolynomialQ : [-243 1620 -4320 5760 -3840 1024]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 10
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PolynomialP : [497]
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PolynomialQ : [-1 20 -160 640 -1280 1024]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 6
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PolynomialP : [3199]
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PolynomialQ : [-1 10 -40 80 -80 32]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2004832
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 0
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PolynomialP : [777]
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PolynomialQ : [0 0 0 0 0 1]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -20
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PowerShift : 27
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PolynomialP : [369]
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PolynomialQ : [-16807 96040 -219520 250880 -143360 32768]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -20
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PowerShift : 22
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PolynomialP : [369]
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PolynomialQ : [-3125 25000 -80000 128000 -102400 32768]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -20
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PowerShift : 17
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PolynomialP : [369]
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PolynomialQ : [-243 3240 -17280 46080 -61440 32768]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -20
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PowerShift : 12
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PolynomialP : [369]
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PolynomialQ : [-1 40 -640 5120 -20480 32768]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 62651
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Alternating : "false"
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PowerCoef : -20
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PowerShift : 10
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PolynomialP : [369]
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PolynomialQ : [-1 10 -40 80 -80 32]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2004832
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Alternating : "false"
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PowerCoef : -20
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PowerShift : 0
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PolynomialP : [369]
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PolynomialQ : [0 0 0 0 0 1]
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}}]
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]
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}
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}
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