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Lemniscate - Zuniga (2023-vi) (G2).cfg
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Lemniscate - Zuniga (2023-vi) (G2).cfg
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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: October 3, 2023
//
// Value: 5.24411510858423962092967917978223882736550990286324...
//
// Pair-wise term merge of Zuniga (2023-vi).
//
// _ _
// inf ( (-1/16777216)^n P(n) | 1/8 3/8 5/8 7/8 3/16 7/16 11/16 15/16 | )
// 2 omega = SUM ( ----------------------------------------------------- | | )
// n=1 ( (8n-1)(8n-3)(8n-5)(8n-7)(16n-1)(16n-5)(16n-9)(16n-13) |_1/32 5/32 9/32 13/32 17/32 21/32 25/32 29/32_|n )
// _
// Or
//
// inf ( P(n) k=n ( (8k-1)(8k-3)(8k-5)(8k-7)(16k-1)(16k-5)(16k-9)(16k-13) ) )
// 2 omega = SUM ( ----------------------------------------------------- PROD (-------------------------------------------------------------------- ) )
// n=1 ( (8n-1)(8n-3)(8n-5)(8n-7)(16n-1)(16n-5)(16n-9)(16n-13) k=1 ( 4096 (32k-3)(32k-7)(32k-11)(32k-15)(32k-19)(32k-23)(32k-27)(32k-31) ) )
//
//
// P(n) = 750599893155840*n^7 - 2465512126676992*n^6 + 3305810396971008*n^5 - 2327426831319040*n^4 + 919690491432960*n^3 - 201024828994048*n^2
// + 22012514018112*n - 897181286400
//
// _ _
// | 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 = w (w + 1) (w + 2) .... (w + n - 1)
//
// Cost = 1.9236
//
{
NameShort : "Lemniscate"
NameLong : "Lemniscate Constant"
AlgorithmShort : "Zuniga (2023-vi) (G2)"
AlgorithmLong : "Zuniga (2023-vi) (G2)"
Formula : {
SeriesHypergeometric : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1
PolynomialP : [-897181286400 22012514018112 -201024828994048 919690491432960 -2327426831319040 3305810396971008 -2465512126676992 750599893155840]
PolynomialQ : [5191227740160 -132757746352128 1295394533277696 -6528933331730432 18990172129460224 -33102996577452032 34111248740122624 -19140298416324608 4503599627370496]
PolynomialR : [61425 -2187840 28340096 -179896320 635080704 -1309409280 1566572544 -1006632960 268435456]
}
}
}