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

• Опубліковано в: Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2016
• ISSN: 1815-0659
• Автор: Volkmer, H.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2016
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/147735
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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).