Preprint Article Version 1 This version is not peer-reviewed

New Two Parameter Gamma Function

Version 1 : Received: 30 April 2020 / Approved: 30 April 2020 / Online: 30 April 2020 (16:31:51 CEST)

How to cite: Sing Gehlot, K. New Two Parameter Gamma Function. Preprints 2020, 2020040537 (doi: 10.20944/preprints202004.0537.v1). Sing Gehlot, K. New Two Parameter Gamma Function. Preprints 2020, 2020040537 (doi: 10.20944/preprints202004.0537.v1).

Abstract

In this paper we introduce the New/Generalized two parameter Gamma function and Pochhammer symbol. We named them, as Generalized p - k Gamma Function and Generalized p - k Pochhammer symbol and denoted as $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ respectively. We prove the several identities for $ _{p}^{a}\Gamma_{k}(x) $ and $ _{p}^{a}(x)_{n,k} $ those satisfied by the classical Gamma function. Also we provide the integral representation for the $ _{p}^{a}\Gamma_{k}(x) $

Subject Areas

New/Generalized two parameter Gamma function; New/Generalized two parameter Pochhammer symbol; Two Parameter Pochhammer symbol; Two parameter Gamma function; New/Generalized two parameter Psi function; New/Generalized p - k Hypergeometric function

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