On a function of Ramanujan twisted by a logarithm
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915137216053248 |
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| author | Dixit, Atul Sathyanarayana, Sumukha Sharan, N. Guru |
| author_facet | Dixit, Atul Sathyanarayana, Sumukha Sharan, N. Guru |
| contents | A two-term functional equation for an infinite series involving the digamma function and a logarithmic factor is derived. A modular relation on page 220 of Ramanujan's Lost Notebook as well as a corresponding recent result for the derivative of Deninger's function are two main ingredients in its derivation. An interesting integral $\mathscr{H}(x)$, which is of independent interest, plays a prominent role in our functional equation. Several alternative representations for $\mathscr{H}(x)$ are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02419 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a function of Ramanujan twisted by a logarithm Dixit, Atul Sathyanarayana, Sumukha Sharan, N. Guru Number Theory Classical Analysis and ODEs Primary 11F03, Secondary 33B15 A two-term functional equation for an infinite series involving the digamma function and a logarithmic factor is derived. A modular relation on page 220 of Ramanujan's Lost Notebook as well as a corresponding recent result for the derivative of Deninger's function are two main ingredients in its derivation. An interesting integral $\mathscr{H}(x)$, which is of independent interest, plays a prominent role in our functional equation. Several alternative representations for $\mathscr{H}(x)$ are obtained. |
| title | On a function of Ramanujan twisted by a logarithm |
| topic | Number Theory Classical Analysis and ODEs Primary 11F03, Secondary 33B15 |
| url | https://arxiv.org/abs/2502.02419 |