maxframe.tensor.special.gammainc#

maxframe.tensor.special.gammainc(a, x, out=None)[source]#

Regularized lower incomplete gamma function.

It is defined as

\[P(a, x) = \frac{1}{\Gamma(a)} \int_0^x t^{a - 1}e^{-t} dt\]

for \(a > 0\) and \(x \geq 0\). See [dlmf] for details.

Parameters:

  • a (array_like) – Positive parameter

  • x (array_like) – Nonnegative argument

  • out (ndarray, optional) – Optional output array for the function values

Returns:

Values of the lower incomplete gamma function

Return type:

scalar or ndarray

See also

gammaincc

regularized upper incomplete gamma function

gammaincinv

inverse of the regularized lower incomplete gamma function

gammainccinv

inverse of the regularized upper incomplete gamma function

Notes

The function satisfies the relation gammainc(a, x) + gammaincc(a, x) = 1 where gammaincc is the regularized upper incomplete gamma function.

The implementation largely follows that of [boost].

References

[dlmf]

NIST Digital Library of Mathematical functions https://dlmf.nist.gov/8.2#E4