Lerch Asymptotics

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Olde Daalhuis, Adri B.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212172
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Lerch Asymptotics. Adri B. Olde Daalhuis. SIGMA 20 (2024), 023, 9 pages

We use a Mellin-Barnes integral representation for the Lerch transcendent (, , ) to obtain large asymptotic approximations. The simplest divergent asymptotic approximation terminates in the case that is an integer. For non-integer , the asymptotic approximations consist of the sum of two series. T...