Catalan Numbers in Terms of $(\alpha, k)-$Gamma Function and $(\alpha, k)-$Beta Function

Abstract

In the paper, the authors discuss some extended results involving the Catalan numbers and establish an integral representation of the Catalan numbers in terms of the $(\alpha,k)$-gamma and $(\alpha,k)$-beta function. We refer to the results available in the literature by giving special values to the parameters in the obtained theorems.