Showing papers on "q-gamma function published in 2012"
Posted Content•
TL;DR: In this paper, the authors defined a generalized version of the gamma function, called the gamma-p,q function, which is a generalization of the Gamma function and gave some properties related to convexity, log-convexity and completely monotonic function.
Abstract: It is defined $\Gamma_{p,q}$ function, a generalize of $\Gamma$ function. Also, we defined $\psi_{p,q}$-analogue of the psi function as the log derivative of $\Gamma_{p,q}$. For the $\Gamma_{p,q}$ -function, are given some properties related to convexity, log-convexity and completely monotonic function. Also, some properties of $\psi_{p,q} $ analog of the $\psi$ function have been established. As an application, when $p\to \infty, q\to 1,$ we obtain all result of \cite{Valmir1} and \cite{SHA}.
25 citations
TL;DR: In this paper, the authors extended the concept of q-special functions of complex variable to Q-special matrix functions through the study of a Q-gamma and a q-beta matrix function.
Abstract: The main goal of this article is to extend the concept of q-special functions of complex variable to q-special matrix functions through the study of a q-gamma and a q-beta matrix function. The q-shifted factorial, q-gamma and q-beta matrix functions are defined and some of their properties are investigated.
14 citations
TL;DR: In this article, the neutrix and neutrix limit is used to obtain some equalities of the q-gamma function for all real values of x, where x > 0, 0 < q < 0, and q < 1.
Abstract: The q-analogue of the gamma function is defined by Γq (x) for x > 0, 0 < q <
1. In this work the neutrix and neutrix limit are used to obtain some
equalities of the q-gamma function for all real values of x.
TL;DR: In this article, the authors retrospect and analyse Wen- del's double inequality, Kazarino's renement of Wallis' formula, Watson's monotonicity, Gautschi's double inequalities, Kershaw's rst double inequality and the (logarithmically) complete monotonic results of functions involving ratios of two gamma or q-gamma functions obtained by Bustoz, Ismail, Lorch, Muldoon, and other mathematicians.
Abstract: In the survey paper, along one of several main lines of bounding the ratio of two gamma functions, the authors retrospect and analyse Wen- del's double inequality, Kazarino's renement of Wallis' formula, Watson's monotonicity, Gautschi's double inequality, Kershaw's rst double inequality, and the (logarithmically) complete monotonicity results of functions involving ratios of two gamma or q-gamma functions obtained by Bustoz, Ismail, Lorch, Muldoon, and other mathematicians.
Journal Article•
TL;DR: In this article, the (q1, , qs)-analogues of those inequalities were presented, where the gamma functions were assumed to be (q 1, q 2, q 3 ).
Abstract: Recently were established q-analogues of some inequalities involving the gamma functions In this paper are presented the (q1, , qs)-analogues of those inequalities