CERTAIN INEQUALITIES INVOLVING THE Q-DEFORMED GAMMA FUNCTION

This paper is inspired by the work of J. Sandor in 2006. In the paper, the authors establish some double inequalities involving the ratio Gamma(q)(x+1)/Gamma(q)(x+1/2), where Gamma(q)(x) is the q-deformation of the classical Gamma function denoted by Gamma(x). The method employed in presenting the results makes use of Jackson's q-integral representation of the g-deformed Gamma function. In addition, Holder's inequality for the q-integral, as well as some basic analytical techniques involving the q-analogue of the psi function are used. As a consequence, q-analogues of the classical Wendel's asymptotic relation are obtained. At the end, sharpness of the inequalities established in this paper is investigated.