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https://github.com/opelly27/Y-Cruncher.git
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opelly27
63 lines
2.0 KiB
INI
63 lines
2.0 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: Carl Stormer's 4-term formula
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//
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// Pi = 176 ArcTan(1/57) + 28 ArcTan(1/239) - 48 ArcTan(1/682) + 96 ArcTan(1/12943)
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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 : "Stormer"
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AlgorithmLong : "Stormer's 4-term formula"
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Formula : {
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LinearCombination : [
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[5016 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 1625
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PolynomialP : [0 1]
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PolynomialQ : [1625 3250]
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PolynomialR : [0 1]
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}}]
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[3346 {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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[-32736 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 465125
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PolynomialP : [0 2]
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PolynomialQ : [465125 930250]
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PolynomialR : [0 2]
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}}]
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[621264 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 83760625
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PolynomialP : [0 1]
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PolynomialQ : [83760625 167521250]
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PolynomialR : [0 1]
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}}]
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]
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}
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}
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