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opelly27
40 lines
1.2 KiB
INI
40 lines
1.2 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".
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//
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// y-cruncher custom custom:"constant - algorithm"
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//
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//
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// Author: Alexander J. Yee
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// Date: September 29, 2018
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//
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// Value: 0.91596559417721901505460351493238411077414937428167...
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//
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// Formula by Pilehrood (2010):
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//
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// 1 inf ( 256^k (580k^2 - 184k + 15) (2k)!^3 (3k)!^2 )
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// Catalan = ---- SUM (--------------------------------------------)
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// 64 k=0 ( k^3 (2k-1) (6k)!^2 )
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//
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// https://hal.inria.fr/hal-00990465/document
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// http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_pilehrood_short
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//
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{
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NameShort : "Catalan"
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NameLong : "Catalan's Constant"
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AlgorithmShort : "Pilehrood (short)"
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AlgorithmLong : "Pilehrood (2010) (short)"
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Formula : {
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SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2
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PolynomialP : [15 -184 580]
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PolynomialQ : [225 -3240 14904 -23328 11664]
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PolynomialR : [0 0 0 -32 64]
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}
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}
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}
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