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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)! )
+//
+//    This is not efficient because it computes Pi twice.
+//
+
+{
+    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 {Multiply : [
+                {Log : {
+                    LinearCombination : [
+                        [1 2]
+                        [1 {Sqrt : 3}]
+                    ]
+                }}
+                {Shift : [{Pi : {}} -3]}
+            ]}]
+        ]
+    }
+}