maths.gamma

Gamma function is a very useful tool in math and physics. It helps calculating complex integral in a convenient way. for more info: https://en.wikipedia.org/wiki/Gamma_function In mathematics, the gamma function is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers Python’s Standard Library math.gamma() function overflows around gamma(171.624).

Attributes

num

Functions

gamma_iterative(→ float)

Calculates the value of Gamma function of num

gamma_recursive(→ float)

Calculates the value of Gamma function of num

integrand(→ float)

Module Contents

maths.gamma.gamma_iterative(num: float) → float

Calculates the value of Gamma function of num where num is either an integer (1, 2, 3..) or a half-integer (0.5, 1.5, 2.5 …).

>>> gamma_iterative(-1)
Traceback (most recent call last):
    ...
ValueError: math domain error
>>> gamma_iterative(0)
Traceback (most recent call last):
    ...
ValueError: math domain error
>>> gamma_iterative(9)
40320.0
>>> from math import gamma as math_gamma
>>> all(.99999999 < gamma_iterative(i) / math_gamma(i) <= 1.000000001
...     for i in range(1, 50))
True
>>> gamma_iterative(-1)/math_gamma(-1) <= 1.000000001
Traceback (most recent call last):
    ...
ValueError: math domain error
>>> gamma_iterative(3.3) - math_gamma(3.3) <= 0.00000001
True
maths.gamma.gamma_recursive(num: float) → float

Calculates the value of Gamma function of num where num is either an integer (1, 2, 3..) or a half-integer (0.5, 1.5, 2.5 …). Implemented using recursion Examples: >>> from math import isclose, gamma as math_gamma >>> gamma_recursive(0.5) 1.7724538509055159 >>> gamma_recursive(1) 1.0 >>> gamma_recursive(2) 1.0 >>> gamma_recursive(3.5) 3.3233509704478426 >>> gamma_recursive(171.5) 9.483367566824795e+307 >>> all(isclose(gamma_recursive(num), math_gamma(num)) … for num in (0.5, 2, 3.5, 171.5)) True >>> gamma_recursive(0) Traceback (most recent call last):

…

ValueError: math domain error >>> gamma_recursive(-1.1) Traceback (most recent call last):

…

ValueError: math domain error >>> gamma_recursive(-4) Traceback (most recent call last):

…

ValueError: math domain error >>> gamma_recursive(172) Traceback (most recent call last):

…

OverflowError: math range error >>> gamma_recursive(1.1) Traceback (most recent call last):

…

NotImplementedError: num must be an integer or a half-integer

maths.gamma.integrand(x: float, z: float) → float
maths.gamma.num = 1.0