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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: Kikuo Takano's 4-term formula
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//
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// Pi = 48 ArcTan(1/49) + 128 ArcTan(1/57) - 20 ArcTan(1/239) + 48 ArcTan(1/110443)
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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 : "Takano"
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AlgorithmLong : "Takano's 4-term Formula"
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Formula : {
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LinearCombination : [
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[1176 {SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 1
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CoefficientD : 1201
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PolynomialP : [0 1]
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PolynomialQ : [1201 2402]
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PolynomialR : [0 1]
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}}]
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[3648 {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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[-2390 {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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[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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]
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}
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}
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