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opelly27
39 lines
1.2 KiB
INI
39 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 30, 2018
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//
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// Value: 1.20205690315959428539973816151144999076498629234049...
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//
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// Formula: Mohamud Mohammed (2005)
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//
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// 1 inf ( (-1)^k (2k)!^3 (k + 1)!^6 P(k) )
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// Zeta(3) = --- SUM (--------------------------------)
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// 2 k=0 ( (k + 1)^2 (3k + 3)!^4 )
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//
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// P(k) = 40885k^5 + 124346k^4 + 150160k^3 + 89888k^2 + 26629k + 3116
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//
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{
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NameShort : "Zeta(3)"
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NameLong : "Zeta(3) - Apery's Constant"
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AlgorithmShort : "Mohammed"
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AlgorithmLong : "Mohammed (2005)"
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Formula : {
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SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 3116
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CoefficientD : 2592
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PolynomialP : [0 0 0 -24928 -63464 259952 756384 -712080 -3021000 -364496 4033184 2616640]
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PolynomialQ : [-1296 -23328 -180792 -787320 -2106081 -3542940 -3661038 -2125764 -531441]
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PolynomialR : [0 0 0 -8 32 -8 -80 32 64]
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}
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}
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}
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