Add files via upload

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:    September 29, 2018
+//
+//    Value: 0.91596559417721901505460351493238411077414937428167...
+//
+//    Formula by A. Lupas (2000):
+//
+//                1  inf ( (-1)^(k-1) 256^k (40k^2 - 24k + 3) (2k)!^3 k!^2 )
+//    Catalan = ---- SUM (-------------------------------------------------)
+//               64  k=0 (               k^3 (2k-1) (4k)!^2                )
+//
+//    http://www.lacim.uqam.ca/~plouffe/articles/alupas1.pdf
+//
+
+{
+    NameShort : "Catalan"
+    NameLong : "Catalan's Constant"
+    AlgorithmShort : "Lupas"
+    AlgorithmLong : "Lupas (2000)"
+    Formula : {
+        SeriesHypergeometric : {
+            CoefficientP : 1
+            CoefficientQ : 19
+            CoefficientD : 18
+            PolynomialP : [0 0 0 -608 -576 2304 2560]
+            PolynomialQ : [-9 -96 -352 -512 -256]
+            PolynomialR : [0 0 0 -32 64]
+        }
+    }
+}