On the computation of the incomplete gamma functions for large values of the parameters.

*(English)*Zbl 0616.41028Algorithms for approximation, Proc. IMA Conf., Shrivenham/Engl. 1985, Inst. Math. Appl. Conf. Ser., New Ser. 10, 479-489 (1987).

[For the entire collection see Zbl 0607.00009.]

A method for computing incomplete gamma functions is given for the case when the parameters are both positive and large. The method is based on earlier results of the author on uniform asymptotic expansions of these functions. It is concluded that the method may be considered as an addition to Gautschi’s algorithm, which becomes inefficient in the case that the method described here is best applicable.

##### MSC:

41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |