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:    February 26, 2018
+//
+//    Value: 0.83462684167407318628142973279904680899399301349034...
+//
+//                              1
+//    Gauss's Constant = -----------------
+//                        AGM(1, sqrt(2))
+//
+//
+//    The formula used here is derived from Brown's 2009 formula
+//    for Gamma(1/4).
+//
+//    Source: http://iamned.com/math/infiniteseries.pdf
+//
+
+{
+    NameShort : "Gauss"
+    NameLong : "Gauss's Constant"
+    AlgorithmShort : "Series"
+    AlgorithmLong : "Hypergeometric Series"
+    Formula : {
+        Multiply : [
+            {SeriesHypergeometric : {
+                CoefficientP : 1
+                CoefficientQ : 147
+                CoefficientD : 1
+                PolynomialP : [15435 -143136 20224 1241088 -856064 -2752512 2621440]
+                PolynomialQ : [0 0 82944 331776 331776]
+                PolynomialR : [105 -1408 5504 -8192 4096]
+            }}
+            {Invsqrt : 31104}
+        ]
+    }
+}