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Zbl 0961.33003
López, José L.
Asymptotic expansions of the Whittaker functions for large order parameter. (English)
[J] Methods Appl. Anal. 6, No.2, 249-256 (1999). ISSN 1073-2772

In this paper the asymptotic expansion of the Whittaker function $M_{\kappa, \mu}(z)$ for bounded values of $z\ne 0$ and $\mu$ and large values of $\kappa$ in inverse powers of $\sqrt\kappa$ is derived. An estimate of the remainder is given too. The expansion is not uniform, but it is useful for applications, since the coefficients of the expansion can be calculated in a simple way.
[H.-J.Glaeske (Jena)]

MSC 2000:: *33C15 Confluent hypergeometric functions
41A60 Asymptotic problems in approximation

Keywords: asymptotic expansion; Whittaker function

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