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

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

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