Bull. Korean Math. Soc. 2014; 51(4): 1155-1161
Printed July 31, 2014
https://doi.org/10.4134/BKMS.2014.51.4.1155
Copyright © The Korean Mathematical Society.
Won Sang Chung, Taekyun Kim, and Toufik Mansour
Gyeongsang National University, Kwangwoon University, University of Haifa
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
2018; 55(6): 1755-1771
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