On hypergeometric functions and Pochhammer $k$-symbol

Details On hypergeometric functions and Pochhammer $k$-symbol On hypergeometric functions and Pochhammer $k$-symbol

2004-05-31

arxiv.org/abs/math/0405596v2

Divulgaciones Matematicas. Vol.15. No.2 (2007), pp. 179-192

Mathematics

Classical Analysis and ODEs

12 pages, 3 figures

Scientific paper

We introduce the $k$-generalized gamma function $\Gamma_k$, 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 $\Gamma_k$ and
$B_k$ functions.

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