An algorithm for the evaluation of the incomplete gamma function and the first two partial derivatives with respect to the parameter

A simple to use, straight coded, Fortran 4 algorithm, is presented. This algorithm has the ability to:

1) evaluate the Incomplete Gamma function, Y(r,λx), for parameter values in the range 0 < r < 20.0 and upper limit of integration values in the range 0 75.0;

2) evaluate both the first and second partial derivatives of y with respect to the parameter

3) evaluate both the Euler Di and Trigamma functions, ψ(r) and if ψ′(r)for 0 In all cases the accuracy is nine or more significant figures. The user has several choices of data output format