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We introduce the k-generalized gamma function Γₖ, beta function Bₖ, and Pochhammer k-symbol (x) ₍, ₊. We prove several identities generalizing those satisfied by the classical gamma function, beta function and Pochhammer symbol. We provided integral representation for the Γₖ and Bₖ functions.
Díaz et al. (Mon,) studied this question.