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Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions. (English) Zbl 1195.65025
Summary: Expansions in terms of Bessel functions are considered of the Kummer function ${}_{1}{F}_{1}\left(a;c,z\right)$ (or confluent hypergeometric function) as given by F. Tricomi [Ann. Mat. Pura Appl., IV. Ser. 26, 141–175 (1947; Zbl 0034.33704)] and H. Buchholz [The confluent hypergeometric function with special emphasis on its applications. Berlin-Heidelberg-New York: Springer-Verlag (1969; Zbl 0169.08501)]. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic behavior of these polynomials for large degree is given. Tables are given to show the rate of approximation of the asymptotic estimates. The numerical performance of the expansions is discussed together with the numerical stability of recurrence relations to compute the polynomials. The asymptotic character of the expansions is explained for large values of the parameter $a$ of the Kummer function.
##### MSC:
 65D20 Computation of special functions, construction of tables
##### References:
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