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Lemniscate - Zuniga (2023-v).cfg
55 lines (54 loc) · 2.15 KB
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Lemniscate - Zuniga (2023-v).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 (slightly optimized by Alex Yee)
// Date: September 28, 2023
//
// Value: 5.24411510858423962092967917978223882736550990286324...
//
// _ _
// Sqrt(2) inf ( (27/50000)^n P(n) | 1/4 3/4 7/12 11/12 | )
// 2 omega = ----------- SUM (---------------------------- | | )
// 3 n=1 ( (4n-1)(4n-3)(12n-1)(12n-5) |_ 1/20 9/20 13/20 17/20 _|n )
//
// Or
// inf ( P(n) k=n ( 3(4k-1)(4k-3)(12k-1)(12k-5) ) )
// 2 omega = Sqrt(2) SUM (----------------------------- PROD (-----------------------------------) )
// n=1 ( 3(4n-1)(4n-3)(12n-1)(12n-5) k=1 ( 80(20k-3)(20k-7)(20k-11)(20k-19) ) )
//
//
// P(n) = 2326016*n^3 - 2421504*n^2 + 751456*n - 66048
//
// _ _
// | 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 = 2.1265
//
{
NameShort : "Lemniscate"
NameLong : "Lemniscate Constant"
AlgorithmShort : "Zuniga (2023-v)"
AlgorithmLong : "Zuniga (2023-v)"
Formula : {
Multiply : [
{SeriesHypergeometric : {
CoefficientP : 1
CoefficientQ : 0
CoefficientD : 1
PolynomialP : [-132096 1502912 -4843008 4652032]
PolynomialQ : [351120 -4352000 16960000 -25600000 12800000]
PolynomialR : [45 -888 4992 -10368 6912]
}}
{Invsqrt : 2}
]
}
}