Issue Closed #218 Create Lanczos_approximation

maths/lanczos_approximation.dart

@@ -0,0 +1,35 @@
+import 'dart:math';
+
+double gamma(double x) {
+  const double pi = 3.141592653589793;
+  if (x < 0.5) {
+    return pi / (sin(pi * x) * gamma(1 - x));
+  }
+  x -= 1;
+  double a = 0.99999999999980993;
+  const List<double> p = [
+    676.5203681218851, -1259.1392167224028, 771.32342877765313,
+    -176.61502916214059, 12.507343278686905, -0.13857109526572012,
+    9.9843695780195716e-6, 1.5056327351493116e-7
+  ];
+  for (int i = 0; i < p.length; i++) {
+    a += p[i] / (x + i + 1);
+  }
+  double t = x + p.length - 0.5;
+  return sqrt(2 * pi) * pow(t, x + 0.5) * exp(-t) * a;
+}
+
+double factorial(num n) {
+  if (n is int) {
+    assert(n >= 0, "Factorial of a negative number does not exist");
+  }
+  return gamma(n + 1);
+}
+
+double signedFactorial(int n) {
+  if (n % 2 == 0) {
+    return factorial(n);
+  } else {
+    return -factorial(n);
+  }
+}