Lerch Asymptotics
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212172 |
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| 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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. The first one is in powers of (ln )⁻¹ and the second one is in powers of ⁻¹. Although the second series converges, it is completely hidden in the divergent tail of the first series. We use resummation and optimal truncation to make the second series visible.
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| ISSN: | 1815-0659 |