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opelly27
2021-11-11 21:34:46 -08:00
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Custom Formulas/Zeta(5) - Broadhurst.cfg
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// y-cruncher Custom Formula File
//
// This can be loaded directly from the Custom Compute menu or
// entered from the command line as "custom:filename.cfg".
// y-cruncher custom custom:"filename.cfg"
//
//
// Author: Alexander J. Yee
// Date: October 2, 2018
//
// Value = 1.03692775514336992633136548645703416805708091950191...
//
// Formula: Broadhurst (1998)
// https://arxiv.org/pdf/math/9803067.pdf
//
// 1152 inf 1 ( 248 12912 124 24848 62 3228 31 74552 )
// Zeta(5) = ------- SUM ------ (---------- - ---------- - ---------- - ---------- - ---------- - ---------- + ---------- + ----------)
// 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 )
//
// 7 inf 1 ( 177152 145408 22144 29248 2768 2272 346 111 )
// + -------- SUM -------- (---------- + ---------- - ---------- - ---------- - ---------- + ---------- + ---------- - ----------)
// 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 )
//
// 369 inf 1 ( 131072 4096 1024 128 4 1 )
// + ---------- SUM --------- (- ---------- + ---------- + ---------- + ---------- - ---------- - ----------)
// 64154624 k=0 2^(20k) ( (8k+1)^5 (8k+3)^5 (8k+4)^5 (8k+5)^5 (8k+7)^5 (8k+8)^5 )
//
{
NameShort : "Zeta(5)"
NameLong : "Zeta(5)"
AlgorithmShort : "Broadhurst"
AlgorithmLong : "Broadhurst (1998)"
Formula : {
LinearCombination : [
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "false"
PowerCoef : -4
PowerShift : 14
PolynomialP : [9]
PolynomialQ : [-16807 96040 -219520 250880 -143360 32768]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "false"
PowerCoef : -4
PowerShift : 13
PolynomialP : [9]
PolynomialQ : [-3125 25000 -80000 128000 -102400 32768]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "false"
PowerCoef : -4
PowerShift : 12
PolynomialP : [9]
PolynomialQ : [-243 3240 -17280 46080 -61440 32768]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2021
Alternating : "false"
PowerCoef : -4
PowerShift : 11
PolynomialP : [9]
PolynomialQ : [-1 40 -640 5120 -20480 32768]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -4
PowerShift : 10
PolynomialP : [7263]
PolynomialQ : [-243 1620 -4320 5760 -3840 1024]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -4
PowerShift : 8
PolynomialP : [7263]
PolynomialQ : [-1 20 -160 640 -1280 1024]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -4
PowerShift : 5
PolynomialP : [13977]
PolynomialQ : [-1 10 -40 80 -80 32]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 125302
Alternating : "false"
PowerCoef : -4
PowerShift : 0
PolynomialP : [83871]
PolynomialQ : [0 0 0 0 0 1]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -12
PowerShift : 20
PolynomialP : [1211]
PolynomialQ : [-16807 96040 -219520 250880 -143360 32768]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -12
PowerShift : 17
PolynomialP : [1211]
PolynomialQ : [-3125 25000 -80000 128000 -102400 32768]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -12
PowerShift : 14
PolynomialP : [1211]
PolynomialQ : [-243 3240 -17280 46080 -61440 32768]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -12
PowerShift : 11
PolynomialP : [1211]
PolynomialQ : [-1 40 -640 5120 -20480 32768]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -12
PowerShift : 16
PolynomialP : [497]
PolynomialQ : [-243 1620 -4320 5760 -3840 1024]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -12
PowerShift : 10
PolynomialP : [497]
PolynomialQ : [-1 20 -160 640 -1280 1024]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -12
PowerShift : 6
PolynomialP : [3199]
PolynomialQ : [-1 10 -40 80 -80 32]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2004832
Alternating : "false"
PowerCoef : -12
PowerShift : 0
PolynomialP : [777]
PolynomialQ : [0 0 0 0 0 1]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -20
PowerShift : 27
PolynomialP : [369]
PolynomialQ : [-16807 96040 -219520 250880 -143360 32768]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -20
PowerShift : 22
PolynomialP : [369]
PolynomialQ : [-3125 25000 -80000 128000 -102400 32768]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -20
PowerShift : 17
PolynomialP : [369]
PolynomialQ : [-243 3240 -17280 46080 -61440 32768]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -20
PowerShift : 12
PolynomialP : [369]
PolynomialQ : [-1 40 -640 5120 -20480 32768]
}}]
[1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 62651
Alternating : "false"
PowerCoef : -20
PowerShift : 10
PolynomialP : [369]
PolynomialQ : [-1 10 -40 80 -80 32]
}}]
[-1 {SeriesBinaryBBP : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 2004832
Alternating : "false"
PowerCoef : -20
PowerShift : 0
PolynomialP : [369]
PolynomialQ : [0 0 0 0 0 1]
}}]
]
}
}