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Custom Formulas/Lemniscate - Series-Pi.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:    March 2, 2019
+//
+//    Value: 5.24411510858423962092967917978223882736550990286324...
+//
+//
+//    The formula used here is derived from Brown's 2009 formula
+//    for Gamma(1/4).
+//
+//    Source: http://iamned.com/math/infiniteseries.pdf
+//
+
+{
+    NameShort : "Lemniscate"
+    NameLong : "Lemniscate Constant"
+    AlgorithmShort : "Series-Pi"
+    AlgorithmLong : "Series-Pi"
+    Formula : {
+        Multiply : [
+            {SeriesHypergeometric : {
+                CoefficientP : 1
+                CoefficientQ : 147
+                CoefficientD : 1
+                PolynomialP : [15435 -143136 20224 1241088 -856064 -2752512 2621440]
+                PolynomialQ : [0 0 82944 331776 331776]
+                PolynomialR : [105 -1408 5504 -8192 4096]
+            }}
+            {Pi : {Algorithm : "ramanujan"}}
+            {Invsqrt : 7776}
+        ]
+    }
+}