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https://github.com/opelly27/Y-Cruncher.git
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opelly27
306 lines
12 KiB
INI
306 lines
12 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: February 19, 2019
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//
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// Value = 1.03692775514336992633136548645703416805708091950191...
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//
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// Formula: Broadhurst (1998) rearranged as Huvent (2006)
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// http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta/06/05/0002/
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//
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// Huvent's 2006 formula is mathematically the same as Broadhurst's 1998 formula.
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//
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// ***Therefore, Broadhurst's and Huvent's formulas cannot be used as a compute/verify pair.***
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//
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// The use of the optimized 74-term rearrangement by Alex Yee (2018) to pair with either
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// Broadhurst (1998) or Huvent (2006) is also questionable. But the reformulation is
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// significant enough that it can be considered *computationally* independent, though
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// still *mathematically* the same.
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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 (Huvent 2006)"
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AlgorithmLong : "Broadhurst (1998), Huvent (2006)"
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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 : 62651
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Alternating : "true"
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PowerCoef : -10
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PowerShift : 12
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PolynomialP : [369]
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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 : "true"
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PowerCoef : -10
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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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[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 : "true"
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PowerCoef : -10
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PowerShift : 17
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PolynomialP : [369]
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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 : 18
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PolynomialP : [7263]
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PolynomialQ : [-161051 878460 -1916640 2090880 -1140480 248832]
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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 : 1691577
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 20
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PolynomialP : [32635]
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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 : 13
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PolynomialP : [13977]
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PolynomialQ : [-3125 18750 -45000 54000 -32400 7776]
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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 : -12
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PowerShift : 20
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PolynomialP : [9]
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PolynomialQ : [-2476099 15638520 -39507840 49904640 -31518720 7962624]
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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 : 563859
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 18
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PolynomialP : [1051]
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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 : 2021
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 19
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PolynomialP : [9]
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PolynomialQ : [-1419857 10022520 -28298880 39951360 -28200960 7962624]
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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 : 7
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PolynomialP : [83871]
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PolynomialQ : [-32 240 -720 1080 -810 243]
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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 : 1691577
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 17
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PolynomialP : [32635]
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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 : [7263]
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PolynomialQ : [-16807 144060 -493920 846720 -725760 248832]
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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 : -12
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PowerShift : 17
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PolynomialP : [9]
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PolynomialQ : [-371293 3427320 -12654720 23362560 -21565440 7962624]
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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 : 54567
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 6
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PolynomialP : [3187]
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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 : 2021
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 16
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PolynomialP : [9]
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PolynomialQ : [-161051 1756920 -7666560 16727040 -18247680 7962624]
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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 : 12
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PolynomialP : [7263]
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PolynomialQ : [-3125 37500 -180000 432000 -518400 248832]
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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 : 1691577
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 14
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PolynomialP : [32635]
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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 : 3
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PolynomialP : [83871]
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PolynomialQ : [-1 15 -90 270 -405 243]
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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 : -12
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PowerShift : 14
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PolynomialP : [9]
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PolynomialQ : [-16807 288120 -1975680 6773760 -11612160 7962624]
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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 : 563859
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 12
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PolynomialP : [1051]
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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 : 2021
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 13
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PolynomialP : [9]
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PolynomialQ : [-3125 75000 -720000 3456000 -8294400 7962624]
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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 : 5
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PolynomialP : [13977]
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PolynomialQ : [-1 30 -360 2160 -6480 7776]
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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 : 1691577
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 11
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PolynomialP : [32635]
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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 : 8
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PolynomialP : [7263]
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PolynomialQ : [-1 60 -1440 17280 -103680 248832]
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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 : -12
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PowerShift : 11
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PolynomialP : [9]
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PolynomialQ : [-1 120 -5760 138240 -1658880 7962624]
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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 : 1691577
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Alternating : "false"
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PowerCoef : -12
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PowerShift : -5
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PolynomialP : [128125]
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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 : 2021
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Alternating : "false"
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PowerCoef : -12
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PowerShift : 22
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PolynomialP : [9]
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PolynomialQ : [-6436343 33580920 -70081920 73128960 -38154240 7962624]
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}}]
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]
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}
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}
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