The $q$-deformed Gamma function and $q$-deformed polygamma function

Won Sang Chung; Taekyun Kim; Toufik Mansour

doi:10.4134/BKMS.2014.51.4.1155

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(4): 1155-1161

Printed July 31, 2014

https://doi.org/10.4134/BKMS.2014.51.4.1155

The $q$-deformed Gamma function and $q$-deformed polygamma function

Won Sang Chung, Taekyun Kim, and Toufik Mansour

Gyeongsang National University, Kwangwoon University, University of Haifa

Abstract

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Abstract

In this paper, we rederive the identity $\Gamma_q(x)\Gamma_q(1- x) =\frac { \pi_q }{ \sin_q (\pi_q x ) }$. Then, we give $q$-analogue of Gauss' multiplication formula and study representation of $q$-oscillator algebra in terms of the $q$-factorial polynomials.

Keywords: $q$-gamma function, $q$-polygamma function

MSC numbers: 11B68, 33D05, 11B65