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arXiv · 1701.01052

Two Parameter Gamma Function and its Properties

Kuldeep Singh Gehlot
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Abstract

In this paper we introduce the Two Parameter Gamma Function, Beta Function and Pochhammer Symbol. We named them, as p - k Gamma Function, p - k Beta Function and p - k Pochhammer Symbol and denoted as $_{p}\Gamma_{k}(x), $ $_{p}B_{k}(x,y) $ and $_{p}(x)_{n,k} $ respectively. We prove the several identities for $_{p}\Gamma_{k}(x), $ $_{p}B_{k}(x,y) $ and $_{p}(x)_{n,k} $ those satisfied by the classical Gamma, Beta and Pochhammer Symbol. Also we provide the integral representation for the $_{p}\Gamma_{k}(x) $ and $_{p}B_{k}(x,y) $.

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Kuldeep Singh Gehlot. 2017-01-03. Two Parameter Gamma Function and its Properties. https://arxiv.org/abs/1701.01052

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