September 2017 Update

Task/Gamma-function/Zkl/gamma-function-2.zkl

@@ -0,0 +1,28 @@
+fcn lanczosGamma(z) { z = z.toFloat();
+    // Coefficients used by the GNU Scientific Library.
+    // http://en.wikipedia.org/wiki/Lanczos_approximation
+    const g = 7, PI = (0.0).pi;
+    exp := (0.0).e.pow;
+    var table = T(
+             0.99999_99999_99809_93,
+           676.52036_81218_851,
+         -1259.13921_67224_028,
+           771.32342_87776_5313,
+          -176.61502_91621_4059,
+            12.50734_32786_86905,
+            -0.13857_10952_65720_12,
+             9.98436_95780_19571_6e-6,
+             1.50563_27351_49311_6e-7);
+
+    // Reflection formula.
+    if (z < 0.5) {
+        return(PI / ((PI * z).sin() * lanczosGamma(1.0 - z)));
+    } else {
+        z -= 1;
+        x := table[0];
+        foreach i in ([1 .. g + 1]){
+            x += table[i] / (z + i); }
+        t := z + g + 0.5;
+        return((2.0 * PI).sqrt() * t.pow(z + 0.5) * exp(-t) * x);
+    }
+}