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https://github.com/opelly27/Y-Cruncher.git
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opelly27
39 lines
1.1 KiB
INI
39 lines
1.1 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 A. Lupas (2000):
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//
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// 1 inf ( (-1)^(k-1) 256^k (40k ^2 - 24k + 3) (2k)!^3 k!^2 )
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// Catalan = ---- SUM (-------------------------------------------------)
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// 64 k=0 ( k^3 (2k-1) (4k)!^2 )
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//
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// http://www.lacim.uqam.ca/~plouffe/articles/alupas1.pdf
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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 : "Lupas"
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AlgorithmLong : "Lupas (2000)"
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Formula : {
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SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 19
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CoefficientD : 18
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PolynomialP : [0 0 0 -608 -576 2304 2560]
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PolynomialQ : [-9 -96 -352 -512 -256]
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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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