Some properties of the k-Gamma function

Abstract

We give completely monotonicity properties and inequalities for functions involving the Γ_k functions and their logarithmic derivatives ψ_k functions. We introduce a k-analogue of the Riemann Zeta function ζ_k as an integral and using Schwarz’s and Holder’s inequalities we obtain some inequalities relating ζ_k and Γ_k functions. The obtained results are the k-anologues of known results concerning functions involving the Gamma and psi functions.

Keywords

• Γ_k function
• ψ_k function
• ζ_k function
• Completely monotonic functions
• Logarithmically completely monotonic functions
• Inequalities