mirror of
https://github.com/opelly27/Y-Cruncher.git
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opelly27
80 lines
2.8 KiB
INI
80 lines
2.8 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: September 30, 2018
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//
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// Value: 3.14159265358979323846264338327950288419716939937510...
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//
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// Formula: Chien-Lih Hwang's 6-term formula (1997)
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//
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// Pi = 732 ArcTan(1/239) + 128 ArcTan(1/1023) - 272 ArcTan(1/5832)
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// + 48 ArcTan(1/110443) - 48 ArcTan(1/4841182) - 400 ArcTan(1/6826318)
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//
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// This uses Euler's ArcTan formula which is slightly faster
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// than the usual Taylor series.
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//
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{
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NameShort : "Pi"
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NameLong : "Pi"
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AlgorithmShort : "Hwang"
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AlgorithmLong : "Hwang's 6-term Formula (1997)"
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Formula : {
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LinearCombination : [
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[87474 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 28561
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PolynomialP : [0 1]
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PolynomialQ : [28561 57122]
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PolynomialR : [0 1]
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}}]
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[65472 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 523265
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PolynomialP : [0 1]
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PolynomialQ : [523265 1046530]
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PolynomialR : [0 1]
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}}]
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[-1586304 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 34012225
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PolynomialP : [0 2]
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PolynomialQ : [34012225 68024450]
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PolynomialR : [0 2]
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}}]
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[2650632 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 6098828125
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PolynomialP : [0 1]
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PolynomialQ : [6098828125 12197656250]
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PolynomialR : [0 1]
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}}]
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[-232376736 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 23437043157125
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PolynomialP : [0 2]
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PolynomialQ : [23437043157125 46874086314250]
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PolynomialR : [0 2]
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}}]
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[-109221088 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 1863944697485
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PolynomialP : [0 2]
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PolynomialQ : [46598617437125 93197234874250]
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PolynomialR : [0 2]
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}}]
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]
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}
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}
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