Add files via upload

2026-05-20 14:37:38 +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.cfg".
+//      y-cruncher custom custom:"filename.cfg"
+//
+//
+//    Author:  Alexander J. Yee
+//    Date:    October 2, 2018
+//
+//    Value = 0.91596559417721901505460351493238411077414937428167...
+//
+//    Formula: G. Huvent (2006)
+//
+//               3  inf (    1    (    2            2            1     ))
+//    Catalan = --- SUM (-------- (---------- - ---------- + ----------))
+//               4  k=0 ( (-4)^k  ( (4k+1)^2     (4k+2)^2     (4k+3)^2 ))
+//
+//               1   inf (    1     (    8            4            1     ))
+//            - ---- SUM (--------- (---------- + ---------- + ----------))
+//               32  k=0 ( (-64)^k  ( (4k+1)^2     (4k+2)^2     (4k+3)^2 ))
+//
+//
+//    Optimized by Alex Yee (2013) to:
+//
+//                1   inf (    1     (    576           144            72            18
+//    Catalan = ----- SUM (--------- (----------- - ----------- - ----------- - ------------
+//               384  k=0 ( (-64)^k  ( (12k+1)^2     (12k+5)^2     (12k+7)^2     (12k+11)^2
+//
+//                    144           9           64            8            8     ))
+//              - ---------- - ---------- - ---------- - ---------- - ---------- ))
+//                 (6k+1)^2     (6k+5)^2     (4k+1)^2     (4k+3)^2     (2k+1)^2  ))
+//
+//    This implementation combines all the terms into a single massive one.
+//    This mirrors y-cruncher's native implementation.
+//
+
+{
+    NameShort : "Catalan"
+    NameLong : "Catalan's Constant"
+    AlgorithmShort : "Huvent (combined)"
+    AlgorithmLong : "Huvent (2006) (combined)"
+    Formula : {
+        SeriesBinaryBBP : {
+            CoefficientP : -1334025
+            CoefficientQ : 469137217
+            CoefficientD : 512265600
+            Alternating : "true"
+            PowerCoef : -6
+            PowerShift : 0
+            PolynomialP : [
+                -11728430425 -360406957080 -4419704161120 -24153149527360
+                5572409156528 1029713994232704 8098743309464448 36670081182465024
+                113872382317283328 256653109156773888 428868733241327616 532937589964406784
+                486920573914447872 318025249742389248 140614334152704000 37721048963088384
+                4636372233093120
+            ]
+            PolynomialQ : [
+                33350625 2116999500 60083208700 1015899910560
+                11506397536624 93025165344960 558162678313024 2549178063839232
+                9008762620336128 24883108561207296 53971174016925696 91902035745570816
+                122177336673042432 125309104724901888 97123825191223296 54970731296980992
+                21422417343676416 5135673858195456 570630428688384
+            ]
+        }
+    }
+}