2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156756We introduce the $k$-generalized gamma function $Γ_k$, beta function $B_k$, and Pochhammer $k$-symbol $(x)_{n,k}$. We prove several identities generalizing those satisfied by the classical gamma function, beta function and Pochhammer symbol. We provided integral representation for the $Γ_k$ and $B_k$ functions.12 pages, 3 figuresClassical Analysis and ODEsHigh Energy Physics - TheoryQuantum Physicstext