//  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:"GL_Gamma1d8.cfg"
//
//
//    Author:  Gerd Lamprecht (Germany)
//    Date:    Nov 02, 2024
//
//    Value: 7.533941598797611904699229841215...
//
//    Gamma(1/8) = (2 2^(3/4) 3^(9/16)*Pi^(3/8) AGM[1,Sqrt[2]]^(1/4) Sqrt[7 (1+Sqrt[2])*2F1[7/16,15/16,9/8,-192/2209]])/47^(7/16)
//
//
{
    NameShort : "sGamma1d8"
    NameLong : "lGamma1d8"
    AlgorithmShort : "ASGamma1d8"
    AlgorithmLong : "ALGamma1d8"
    Formula : {
    	Scope : {
            Locals : [
                {sqrt2 : {Sqrt : 2}}
            ]
    	    Formula : {
    	    	Multiply : [
    	    	{ Invsqrt : {
			 Multiply : [
	              		{SeriesHypergeometric : {
	                  				Power : -1
	                                    		CoefficientP : 1
	                                    		CoefficientQ : 336
	                                    		CoefficientD : 1
	                                    		PolynomialP : [-211680]
	                                    		PolynomialQ : [0 2209 17672]
	                                    		PolynomialR : [-630 -2112 -1536]
	                         }}
	                         { Invsqrt : {AGM : "sqrt2"}
	                         }
	              		 {InvNthRoot : [8 3]}
	              		 {InvNthRoot : [4 { Power : [{Pi : {}} 3]}]
	    			 }
	              		 {LinearCombination : [
	                                     [1 2]
	                                     [-1 "sqrt2"]
	                         ]}
	              		 
	              		 
	              		 
	                 ]
                }}
                {InvNthRoot : [16 506623120463]}
                ]
           }
       }
    }
}