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

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