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Custom Formulas/Catalan - Guillera (2008).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:"constant - algorithm"
+//
+//
+//    Author:  Alexander J. Yee
+//    Date:    September 29, 2018
+//
+//    Value: 0.91596559417721901505460351493238411077414937428167...
+//
+//    Original formula by Guillera (2008). Optimized as follows:
+//
+//               1  inf ( (-8)^k (3k+2) k!^6 )
+//    Catalan = --- SUM (--------------------)
+//               2  k=0 (      (2k+1)!^3     )
+//
+//    https://arxiv.org/pdf/1104.0396.pdf
+//    http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_guillera
+//
+
+{
+    NameShort : "Catalan"
+    NameLong : "Catalan's Constant"
+    AlgorithmShort : "Guillera (2008)"
+    AlgorithmLong : "Guillera (2008)"
+    Formula : {
+        SeriesHypergeometric : {
+            CoefficientP : 1
+            CoefficientQ : 2
+            CoefficientD : 2
+            PolynomialP : [0 0 0 2 3]
+            PolynomialQ : [-1 -6 -12 -8]
+            PolynomialR : [0 0 0 1]
+        }
+    }
+}