y-cruncher-Formulas/Official Formulas/Log(5) - Zuniga (2024-i).cfg at master · Mysticial/y-cruncher-Formulas · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
//  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:    February 2, 2024
//
//    Value: 1.6094379124341003746007593332261876395.....
//
//                                                  _          _
//               inf (  (-1/675)^n ( 728 n - 124 ) |  1    1/2  |  )
//    Log(3) =   SUM ( --------------------------- |            |  )
//               n=1 (        -2n (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 1.2280
//
//    https://mathoverflow.net/questions/463436/are-these-fast-convergent-series-for-log2-log3-and-log5-already
//
//
{
    NameShort : "Log(5)"
    NameLong : "Log(5)"
    AlgorithmShort : "Zuniga (2024-i)"
    AlgorithmLong : "Zuniga (2024-i)"
    Formula : {
        SeriesHypergeometric : {
            CoefficientP : 1
            CoefficientQ : 0
            CoefficientD : 1
            PolynomialP : [-124 728]
            PolynomialQ : [375 -2700 2700]
            PolynomialR : [0 2 -4]
        }
    }
}