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2026-05-20 05:17:34 +00:00 · 2021-11-11 21:34:46 -08:00
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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:    February 26, 2019
+//
+//    Value: 3.62560990822190831193068515586767200299516768288006...
+//
+//    Source: http://iamned.com/math/infiniteseries.pdf
+//
+//    This file uses Ramanujan's formula for Pi to make it computationally
+//    independent from "Gamma(1d4) - AGM-Pi.cfg".
+//
+
+{
+    NameShort : "Gamma(¼)"
+    NameLong : "Gamma(1/4)"
+    AlgorithmShort : "Series-Pi (Brown)"
+    AlgorithmLong : "Series-Pi (Brown 2009)"
+    Formula : {
+        Invsqrt : {
+            Multiply : [
+                {SeriesHypergeometric : {
+                    Power : -1
+                    CoefficientP : 1
+                    CoefficientQ : 147
+                    CoefficientD : 108
+                    PolynomialP : [15435 -143136 20224 1241088 -856064 -2752512 2621440]
+                    PolynomialQ : [0 0 82944 331776 331776]
+                    PolynomialR : [105 -1408 5504 -8192 4096]
+                }}
+                {Invsqrt : {
+                    LinearCombination : [[
+                        3
+                        {Power : [
+                            {Pi : {Algorithm : "ramanujan"}}
+                            3
+                        ]}
+                    ]]
+                }}
+            ]
+        }
+    }
+}