# 3.5.1.3.42 Incomplete_gamma

## Definition:

$P = incomplete\_gamma(a, x)$ evaluates the incomplete gamma functions in the normalized form

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

$Q(a,x)=\frac 1{\Gamma (a)}\int_x^\infty t^{a-1}e^{-t}dt$

with x ≥ 0 and a > 0, to a user-specified accuracy. With this normalization, P(a, x)+Q(a, x) = 1. The function returns with machine precision as relative accuracy.

For more information please review the s14bac function in the NAG document.

## Parameters:

a (input, double)
The argument a of the function.
Constraint: a > 0.0.
x (input, double)
The argument x of the function.
Constraint: x > 0.0.
P (output, double)
The value of the incomplete gamma functions in the normalized form
     $P(a,x)=\frac 1{\Gamma (a)}\int_0^xt^{a-1}e^{-t}dt$