On some properties of special functions involving $k$-gamma and $k$-digamma functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913703108018176 |
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| author | Yin, Li Zhang, Jumei |
| author_facet | Yin, Li Zhang, Jumei |
| contents | Based on $k$-gamma and $k$-digamma functions, we show four series expansions to the Furdui-type integral related to Riemann zeta function and hypergeometric function, and also present some new identities, series expansions and inequalities on the Hadamard $k$-gamma function and the Nielsen $k$-beta function. Finally, we also pose an open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On some properties of special functions involving $k$-gamma and $k$-digamma functions Yin, Li Zhang, Jumei Classical Analysis and ODEs Number Theory 33B15(Primary), 26A48(Secondary) G.1.2 Based on $k$-gamma and $k$-digamma functions, we show four series expansions to the Furdui-type integral related to Riemann zeta function and hypergeometric function, and also present some new identities, series expansions and inequalities on the Hadamard $k$-gamma function and the Nielsen $k$-beta function. Finally, we also pose an open problem. |
| title | On some properties of special functions involving $k$-gamma and $k$-digamma functions |
| topic | Classical Analysis and ODEs Number Theory 33B15(Primary), 26A48(Secondary) G.1.2 |
| url | https://arxiv.org/abs/2502.15852 |