# mars.tensor.special.gammaincc¶

mars.tensor.special.gammaincc(a, b, **kwargs)[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

Returns

Values of the lower incomplete gamma function

Return type

scalar or ndarray

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].

gammaincc

regularized upper incomplete gamma function

gammaincinv

inverse of the regularized lower incomplete gamma function with respect to x

gammainccinv

inverse of the regularized upper incomplete gamma function with respect to x

References

dlmf

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

boost

Maddock et. al., “Incomplete Gamma Functions”, https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html