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## Remarks & Credit
## https://en.wikipedia.org/wiki/Lanczos_approximation
from cmath import sin, sqrt, pi, exp
p = [676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6,1.5056327351493116e-7]
EPSILON = 1e-07
def drop_imag(z):
if abs(z.imag) <= EPSILON:
z = z.real
return z
def gamma(z):
z = complex(z)
if z.real < 0.5:
y = pi / (sin(pi * z) * gamma(1 - z)) ## Reflection formula
else:
z = z - 1
x = 0.99999999999980993
for (i, pval) in enumerate(p):
x = x + pval / (z + i + 1)
t = z + len(p) - 0.5
y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x
return drop_imag(y)
"""
The above use of the reflection (thus the if-else structure) is necessary, even though
it may look strange, as it allows to extend the approximation to values of z where
Re(z) < 0.5, where the Lanczos method is not valid.
"""
print(gamma(3))
print(gamma(5))
print(gamma(7))
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