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 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.2014.51.4.1155Published 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 Full-Text :