Simple Implementation
The following implementation in the Python programming language works for complex arguments and typically gives 15 correct decimal places:
from cmath import * # Coefficients used by the GNU Scientific Library g = 7 p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7] def gamma(z): z = complex(z) # Reflection formula if z.real < 0.5: return pi / (sin(pi*z)*gamma(1-z)) else: z -= 1 x = p for i in range(1, g+2): x += p/(z+i) t = z + g + 0.5 return sqrt(2*pi) * t**(z+0.5) * exp(-t) * xRead more about this topic: Lanczos Approximation
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