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arXiv · 2502.15852

On some properties of special functions involving $k$-gamma and $k$-digamma functions

Li Yin·Jumei Zhang
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Abstract

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.

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Li Yin, Jumei Zhang. 2025-02-21. On some properties of special functions involving $k$-gamma and $k$-digamma functions. https://arxiv.org/abs/2502.15852

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