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

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2016
• 1. Verfasser: Volkmer, H.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2016
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147735
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: The Asymptotic Expansion of Kummer Functions for Large Values of the α-Parameter, and Remarks on a Paper by Olver / H. Volkmer // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 9 назв. — англ.

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).