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On hypergeometric functions and Pochhammer $k$-symbol

Rafael Diaz·Eddy Pariguan
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Abstract

We 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.

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Rafael Diaz, Eddy Pariguan. 2005-04-19. On hypergeometric functions and Pochhammer $k$-symbol. https://arxiv.org/abs/math/0405596

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