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 |
| Main Author: | |
| 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| _version_ | 1862624017106599936 |
|---|---|
| author | Olde Daalhuis, Adri B. |
| author_facet | Olde Daalhuis, Adri B. |
| citation_txt | Lerch Asymptotics. Adri B. Olde Daalhuis. SIGMA 20 (2024), 023, 9 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-14T14:38:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212172 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T14:38:18Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Olde Daalhuis, Adri B. 2026-01-30T08:18:46Z 2024 Lerch Asymptotics. Adri B. Olde Daalhuis. SIGMA 20 (2024), 023, 9 pages 1815-0659 2020 Mathematics Subject Classification: 11M35; 30E15; 41A30; 41A60 arXiv:2311.11886 https://nasplib.isofts.kiev.ua/handle/123456789/212172 https://doi.org/10.3842/SIGMA.2024.023 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. This research was supported by a research Grant 60NANB20D126 from the National Institute of Standards and Technology. The author thanks the referees for their very helpful comments and suggestions for improving the presentation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lerch Asymptotics Article published earlier |
| spellingShingle | Lerch Asymptotics Olde Daalhuis, Adri B. |
| title | Lerch Asymptotics |
| title_full | Lerch Asymptotics |
| title_fullStr | Lerch Asymptotics |
| title_full_unstemmed | Lerch Asymptotics |
| title_short | Lerch Asymptotics |
| title_sort | lerch asymptotics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212172 |
| work_keys_str_mv | AT oldedaalhuisadrib lerchasymptotics |