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opelly27
41 lines
1.3 KiB
INI
41 lines
1.3 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: 1.20205690315959428539973816151144999076498629234049...
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//
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// Formula: Wedeniwski (1998)
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//
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// 1 inf ( (-1)^k ((2k + 1)! (2k)! k!)^3 P(k) )
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// Zeta(3) = ---- SUM (------------------------------------)
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// 24 k=0 ( (3k + 2)! (4k + 3)!^3 )
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//
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// P(k) = 126392k^5 + 412708k^4 + 531578k^3 + 336367k^2 + 104000k + 12463
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//
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// http://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/Zeta3.txt
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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 : "Wedeniwski"
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AlgorithmLong : "Wedeniwski (1998)"
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Formula : {
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SeriesHypergeometric : {
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CoefficientP : 1
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CoefficientQ : 12463
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CoefficientD : 10368
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PolynomialP : [0 0 0 0 0 -12463 -29222 138077 338328 -427644 -1338144 58480 1784960 1011136]
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PolynomialQ : [-1296 -26568 -230472 -1102080 -3171456 -5621760 -6002688 -3538944 -884736]
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PolynomialR : [0 0 0 0 0 -1 6 -12 8]
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}
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}
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}
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