Explicit Evaluations of Euler Sums Involving Harmonic Numbers with Rational Arguments
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913177325797376 |
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| author | Olaikhan, Ali |
| author_facet | Olaikhan, Ali |
| contents | This paper derives closed-form expressions for four-parameter Euler sums containing generalized harmonic numbers with rational arguments, expressed in terms of the polylogarithm and Lerch transcendent, and reducible (under admissible parameter choices) to Riemann zeta and Hurwitz zeta values. It further obtains closed forms for related polylogarithmic integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit Evaluations of Euler Sums Involving Harmonic Numbers with Rational Arguments Olaikhan, Ali General Mathematics Primary 11M06, 26B15, Secondary 65B10 This paper derives closed-form expressions for four-parameter Euler sums containing generalized harmonic numbers with rational arguments, expressed in terms of the polylogarithm and Lerch transcendent, and reducible (under admissible parameter choices) to Riemann zeta and Hurwitz zeta values. It further obtains closed forms for related polylogarithmic integrals. |
| title | Explicit Evaluations of Euler Sums Involving Harmonic Numbers with Rational Arguments |
| topic | General Mathematics Primary 11M06, 26B15, Secondary 65B10 |
| url | https://arxiv.org/abs/2601.06895 |