`igamma`

Upper incomplete gamma function.

Category: Mathematics > Mathematical Functions

Syntax

Y = igamma(a, x)

Evaluates the integral from x to infinity of t^(a-1)*exp(-t).

Description

This is the unregularized form: igamma(a, 0) is gamma(a). The regularized upper function is gammainc(x, a, 'upper'), which equals igamma(a, x)/gamma(a). For integer a, igamma(a, x) is (a-1)!*exp(-x)*(1 + x + ... + x^(a-1)/(a-1)!), so igamma(2, 1) is 2/e.

Input arguments

a: Shape parameter.
x: Lower limit of the integral, x >= 0 for real results.

Output arguments

Y: Array formed by broadcasting a and x.

Example

Integer shape and the regularized form

igamma(2, 1)
2*exp(-1)
igamma(0.5, [1 2])
gammainc([1 2], 0.5, 'upper')*gamma(0.5)

Output

ans = 0.7358
ans = 0.7358
ans = 1×2

    0.2788    0.0806
ans = 1×2

    0.2788    0.0806

Notes

Complex-valued results (negative arguments) return NaN in MatLivre.

igamma