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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:    September 30, 2018
+//
+//    Value: 1.20205690315959428539973816151144999076498629234049...
+//
+//    Formula: Mohamud Mohammed (2005)
+//
+//               1  inf ( (-1)^k (2k)!^3 (k + 1)!^6 P(k) )
+//    Zeta(3) = --- SUM (--------------------------------)
+//               2  k=0 (     (k + 1)^2 (3k + 3)!^4      )
+//
+//    P(k) = 40885k^5 + 124346k^4 + 150160k^3 + 89888k^2 + 26629k + 3116
+//
+
+{
+    NameShort : "Zeta(3)"
+    NameLong : "Zeta(3) - Apery's Constant"
+    AlgorithmShort : "Mohammed"
+    AlgorithmLong : "Mohammed (2005)"
+    Formula : {
+        SeriesHypergeometric : {
+            CoefficientP : 1
+            CoefficientQ : 3116
+            CoefficientD : 2592
+            PolynomialP : [0 0 0 -24928 -63464 259952 756384 -712080 -3021000 -364496 4033184 2616640]
+            PolynomialQ : [-1296 -23328 -180792 -787320 -2106081 -3542940 -3661038 -2125764 -531441]
+            PolynomialR : [0 0 0 -8 32 -8 -80 32 64]
+        }
+    }
+}