y-cruncher-Formulas/Official Formulas/Log(2) - Zuniga (2024-ii).cfg at master · Mysticial/y-cruncher-Formulas · GitHub

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//  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:"filename.cfg"
//
//    Author:  Jorge Zuniga
//    Date:    January 17, 2024
//
//    Value: 0.69314718055994530941723212145817656807550013436025...
//
//                                                        _          _
//               1   inf (  (1/3888)^n ( 1794 n - 297 )  |  1    1/2  |  )
//    Log(2) = ----- SUM ( ----------------------------- |            |  )
//               2   n=1 (        n (2n-1)               |_1/6   5/6 _|n )
//
//                 _                  _
//                |  a  b  c  ...  z   |        (a)_n  (b)_n  (c)_n  ...  (z)_n
//                |                    |    =   -------------------------------
//                |_ A  B  C  ...  Z  _|n       (A)_n  (B)_n  (C)_n  ...  (Z)_n
//
//
//    (w)_n Pochhammer Symbol.    (w)_n = GAMMA(w + n)/GAMMA(w) = w (w + 1) (w + 2) .... (w + n - 1)
//
//    Cost 0.9679
//
//    https://mathoverflow.net/questions/463436/are-these-fast-convergent-series-for-log2-log3-and-log5-already
//

{
    NameShort : "Log(2)"
    NameLong : "Log(2)"
    AlgorithmShort : "Zuniga (2024-ii)"
    AlgorithmLong : "Zuniga (2024-ii)"
    Formula : {
        SeriesHypergeometric : {
            CoefficientP : 1
            CoefficientQ : 0
            CoefficientD : 2
            PolynomialP : [-297 1794]
            PolynomialQ : [1080 -7776 7776]
            PolynomialR : [0 -1 2]
        }
    }
}