The $q$-deformed Gamma function and $q$-deformed polygamma function
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1155-1161
https://doi.org/10.4134/BKMS.2014.51.4.1155
Published online July 31, 2014
Won Sang Chung, Taekyun Kim, and Toufik Mansour
Gyeongsang National University, Kwangwoon University, University of Haifa
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
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