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2026-05-20 02:57:34 +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:    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]}
+                    ]
+                }
+            }}]
+        ]
+    }
+}