mirror of
https://github.com/opelly27/Y-Cruncher.git
synced 2026-05-20 00:38:45 +00:00
opelly27
40 lines
1.1 KiB
INI
40 lines
1.1 KiB
INI
// y-cruncher Custom Formula File
|
|
//
|
|
// This can be loaded directly from the Custom Compute menu or
|
|
// entered from the command line as "custom:filename".
|
|
//
|
|
// y-cruncher custom custom:"constant - algorithm"
|
|
//
|
|
//
|
|
// Author: Alexander J. Yee
|
|
// Date: September 29, 2018
|
|
//
|
|
// Value: 0.91596559417721901505460351493238411077414937428167...
|
|
//
|
|
// Original formula by Guillera (2008). Optimized as follows:
|
|
//
|
|
// 1 inf ( (-8)^k (3k+2) k!^6 )
|
|
// Catalan = --- SUM (--------------------)
|
|
// 2 k=0 ( (2k+1)!^3 )
|
|
//
|
|
// https://arxiv.org/pdf/1104.0396.pdf
|
|
// http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_guillera
|
|
//
|
|
|
|
{
|
|
NameShort : "Catalan"
|
|
NameLong : "Catalan's Constant"
|
|
AlgorithmShort : "Guillera (2008)"
|
|
AlgorithmLong : "Guillera (2008)"
|
|
Formula : {
|
|
SeriesHypergeometric : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 2
|
|
CoefficientD : 2
|
|
PolynomialP : [0 0 0 2 3]
|
|
PolynomialQ : [-1 -6 -12 -8]
|
|
PolynomialR : [0 0 0 1]
|
|
}
|
|
}
|
|
}
|