math_tools.py 文件源码

def incomplete_gamma_lower(a, x, precision=9):
    # Numerical approximation of the lower incomplete gamma function to the given precision
    # https://en.wikipedia.org/wiki/Incomplete_gamma_function
    # http://mathworld.wolfram.com/IncompleteGammaFunction.html

    max_diff = 10 ** -precision

    def summand(k):
        return ((-x) ** k) / factorial(k) / (a + k)

    xs = x ** a
    sum_ = summand(0)
    prev_value = xs * sum_  # for k=0
    sum_ += summand(1)
    cur_value = xs * sum_  # for k=1
    k = 1
    while abs(cur_value - prev_value) > max_diff:
        k += 1
        prev_value = cur_value
        sum_ += summand(k)
        cur_value = xs * sum_

    return cur_value