Add files via upload

2026-05-20 01:47:34 +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 Pilehrood (2010):
+//
+//                1  inf ( (-256)^k (419840k^6 - 915456k^5 + 782848k^4 - 332800k^3 + 73256k^2 - 7800k + 315) k!^2 (4k)!^4 )
+//    Catalan = ---- SUM (------------------------------------------------------------------------------------------------)
+//               64  k=0 (                         k^3 (2k-1) (4k-1)^2 (4k-3)^2 (8k)!^2 (2k)!                             )
+//
+//    https://hal.inria.fr/hal-00990465/document
+//    http://www.numberworld.org/y-cruncher/internals/binary-splitting-library.html#catalan_pilehrood_long
+//
+
+{
+    NameShort : "Catalan"
+    NameLong : "Catalan's Constant"
+    AlgorithmShort : "Pilehrood (long)"
+    AlgorithmLong : "Pilehrood (2010) (long)"
+    Formula : {
+        SeriesHypergeometric : {
+            CoefficientP : -1
+            CoefficientQ : 0
+            CoefficientD : 2
+            PolynomialP : [315 -7800 73256 -332800 782848 -915456 419840]
+            PolynomialQ : [-11025 295680 -3138304 17219584 -54222848 101711872 -112197632 67108864 -16777216]
+            PolynomialR : [0 0 0 -288 3648 -17408 38912 -40960 16384]
+        }
+    }
+}