SciPy

scipy.special.gammainc

scipy.special.gammainc(a, x) = <ufunc 'gammainc'>

Regularized lower incomplete gamma function.

Defined as

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

for \(a > 0\) and \(x \geq 0\). The function satisfies the relation gammainc(a, x) + gammaincc(a, x) = 1 where gammaincc is the regularized upper incomplete gamma function.

See also

gammaincc
regularized upper incomplete gamma function
gammaincinv
inverse to gammainc versus x
gammainccinv
inverse to gammaincc versus x

Notes

The implementation largely follows that of [R379].

References

[R379](1, 2) Maddock et. al., “Incomplete Gamma Functions”, http://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html