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Task/Gamma-function/Sidef/gamma-function-2.sidef

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+func gamma(z) {
+    var epsilon = 0.0000001
+    func withinepsilon(x) {
+        abs(x - abs(x)) <= epsilon
+    }
+
+    var p = [
+        676.5203681218851,     -1259.1392167224028,
+        771.32342877765313,    -176.61502916214059,
+        12.507343278686905,    -0.13857109526572012,
+        9.9843695780195716e-6,  1.5056327351493116e-7,
+    ]
+
+    var result;
+    z = Complex(z)
+    const pi = Complex.pi
+
+    if (z.real < 0.5) {
+        result = (pi / (sin(pi * z) * gamma(Complex(1) - z)))
+    }
+    else {
+        z -= 1
+        var x = 0.99999999999980993
+
+        p.each_kv { |i, v|
+            x += v/(z + i + 1)
+        }
+
+        var t = (z + p.len - 0.5)
+        result = (sqrt(pi*2) * t**(z+0.5) * exp(-t) * x)
+    }
+
+    withinepsilon(result.im) ? result.real : result
+}
+
+for i in 1..10 {
+    say ("%.14e" % gamma(i/3));
+}