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61 lines
1.3 KiB
Python
61 lines
1.3 KiB
Python
import math
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from scipy.integrate import quad
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from numpy import inf
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def gamma(num: float) -> float:
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"""
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https://en.wikipedia.org/wiki/Gamma_function
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In mathematics, the gamma function is one commonly
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used extension of the factorial function to complex numbers.
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The gamma function is defined for all complex numbers except the non-positive integers
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>>> gamma(-1)
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Traceback (most recent call last):
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...
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ValueError: math domain error
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>>> gamma(0)
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Traceback (most recent call last):
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...
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ValueError: math domain error
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>>> gamma(9)
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40320.0
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>>> from math import gamma as math_gamma
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>>> all(gamma(i)/math_gamma(i) <= 1.000000001 and abs(gamma(i)/math_gamma(i)) > .99999999 for i in range(1, 50))
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True
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>>> from math import gamma as math_gamma
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>>> gamma(-1)/math_gamma(-1) <= 1.000000001
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Traceback (most recent call last):
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...
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ValueError: math domain error
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>>> from math import gamma as math_gamma
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>>> gamma(3.3) - math_gamma(3.3) <= 0.00000001
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True
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"""
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if num <= 0:
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raise ValueError("math domain error")
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return quad(integrand, 0, inf, args=(num))[0]
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def integrand(x: float, z: float) -> float:
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return math.pow(x, z - 1) * math.exp(-x)
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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