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

TL;DR

This paper explores properties of $k$-gamma and $k$-digamma functions, deriving series expansions, identities, and inequalities related to special functions, and poses an open problem for future research.

Contribution

It introduces new series expansions, identities, and inequalities involving $k$-gamma and $k$-digamma functions, expanding the understanding of these special functions.

Findings

Four series expansions for Furdui-type integrals involving $k$-functions

New identities and inequalities for Hadamard $k$-gamma and Nielsen $k$-beta functions

Open problem posed for further investigation

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.