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}.
Categories: math.CA