Some completely monotonic properties for the $(p,q)$-gamma function

Abstract

It is defined ${\Gamma }_{p,q}$ function, a generalize of $\Gamma$ function. Also, we defined ${\psi }_{p,q}$-analogue of the psi function as the log derivative of ${\Gamma }_{p,q}$. For the ${\Gamma }_{p,q}$ -function, are given some properties related to convexity, log-convexity and completely monotonic function. Also, some properties of ${\psi }_{p,q}$ analog of the $\psi$ function have been established. As an application, when $p\to \infty ,q\to 1,$ we obtain all result of \cite{Valmir1} and \cite{SHA}.

12 pages

References in corpus (1)

• $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series

Cited by in corpus (2)

• Some Inequalities for the Ratios of Generalized Digamma Functions
• The $(p,q)$-Analogues of Some Inequalities for the Digamma Function