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2026-05-20 05:17:34 +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.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  ))
+//
+
+{
+    NameShort : "Catalan"
+    NameLong : "Catalan's Constant"
+    AlgorithmShort : "Huvent (optimized)"
+    AlgorithmLong : "Huvent (2006) (optimized)"
+    Formula : {
+        LinearCombination : [
+            [-1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 1
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 5
+                    PolynomialP : [3]
+                    PolynomialQ : [121 -264 144]
+            }}]
+            [1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 1
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 3
+                    PolynomialP : [3]
+                    PolynomialQ : [49 -168 144]
+            }}]
+            [1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 1
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 2
+                    PolynomialP : [3]
+                    PolynomialQ : [25 -120 144]
+            }}]
+            [-1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 1
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 0
+                    PolynomialP : [3]
+                    PolynomialQ : [1 -24 144]
+            }}]
+            [1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 1
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 3
+                    PolynomialP : [3]
+                    PolynomialQ : [25 -60 36]
+            }}]
+            [1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 2
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 0
+                    PolynomialP : [3]
+                    PolynomialQ : [1 -12 36]
+            }}]
+            [1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 3
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 5
+                    PolynomialP : [1]
+                    PolynomialQ : [9 -24 16]
+            }}]
+            [1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 3
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 2
+                    PolynomialP : [1]
+                    PolynomialQ : [1 -8 16]
+            }}]
+            [1 {SeriesBinaryBBP : {
+                    CoefficientP : 1
+                    CoefficientQ : 0
+                    CoefficientD : 3
+                    Alternating : "true"
+                    PowerCoef : -6
+                    PowerShift : 2
+                    PolynomialP : [1]
+                    PolynomialQ : [1 -4 4]
+            }}]
+        ]
+    }
+}