//  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:    November 1, 2018
//
//    Value: 0.91596559417721901505460351493238411077414937428167...
//
//               Pi                      3  inf (      k!^2      )
//    Catalan = ---- Log(2 + sqrt(3)) + --- SUM (----------------)
//               8                       8  k=0 ( (2k+1)^2 (2k)! )
//

{
    NameShort : "Catalan"
    NameLong : "Catalan's Constant"
    AlgorithmShort : "Ramanujan"
    AlgorithmLong : "Ramanujan's Formula"
    Formula : {
        LinearCombination : [
            [1 {SeriesHypergeometric : {
                Power : 1
                CoefficientP : 3
                CoefficientQ : 3
                CoefficientD : 8
                PolynomialP : [0 1]
                PolynomialQ : [-2 -4 8 16]
                PolynomialR : [0 1 4 4]
            }}]
            [1 {Scope : {
                Locals : [
                    {pi : {Pi : {}}}
                    {log2 : {Log : 2}}
                ]
                Formula : {
                    Multiply : [
                        {Log-AGM : {
                            Pi : "pi"
                            Log2 : "log2"
                            Argument : {
                                LinearCombination : [
                                    [1 2]
                                    [1 {Sqrt : 3}]
                                ]
                            }
                        }}
                        {Shift : ["pi" -3]}
                    ]
                }
            }}]
        ]
    }
}