Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 046, 22 pages      arXiv:1601.02263
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications

The Asymptotic Expansion of Kummer Functions for Large Values of the $a$-Parameter, and Remarks on a Paper by Olver

Hans Volkmer
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI, 53201, USA

Received January 10, 2016, in final form May 01, 2016; Published online May 06, 2016

It is shown that a known asymptotic expansion of the Kummer function $U(a,b,z)$ as $a$ tends to infinity is valid for $z$ on the full Riemann surface of the logarithm. A corresponding result is also proved in a more general setting considered by Olver (1956).

Key words: Kummer functions; asymptotic expansions.

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