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.

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