Showing papers on "q-gamma function published in 2014"
TL;DR: In this article, the Stirling formula for the q gamma function is exploited to prove the complete monotonicity property of functions involving the q -gamma and the q-digamma functions.
Abstract: In this paper, the q -analogue of the Stirling formula (the Moak formula) for the q gamma function is exploited to prove the complete monotonicity property of functions involving the q -gamma and the q -digamma functions. The monotonicity of these functions is used to establish sharp inequalities for the q -gamma and the q -polygamma functions and the q -Harmonic number. Mathematics subject classification (2010): 33D05, 26D07, 26A48.
20 citations
TL;DR: In this paper, the series representations of the functions ψp(t), ψq(t) and ψk(t)) were used to prove inequalities involving the ratios Γk(T) Γp(T), Γq(T)) and Γt(T, T ) of the function ψ p(t, ψ q(T).
Abstract: In this paper, we present and prove some inequalities involving the ratios Γk(t) Γp(t) and Γk(t) Γq(t) . Our approach makes use of the series representations of the functions ψp(t), ψq(t) and ψk(t).
10 citations
TL;DR: In this paper, the authors presented some completely monotonic functions involving the polygamma functions, motivated by existing results, and showed that these functions are monotonically monotone.
Abstract: Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
8 citations
TL;DR: This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-No Derivative Works Licens permits non-commercial use, distribution, and reproduction in any medium, provided the original author and source are credited.
7 citations
Journal Article•
TL;DR: In this article, some monotonic functions and inequalities concerning certain ratios of generalized gamma functions are established, and the procedure utilizes the series forms of the generalized digamma functions.
Abstract: In this paper, some monotonic functions and some inequalities concerning certain ratios of generalized gamma functions are established. The procedure utilizes the series forms of the generalized digamma functions.
6 citations
TL;DR: In this paper, some inequalities concerning certain ratios of the classical Euler's Gamma function were presented. The results generalized some recent results, and they were generalized to the Euler Gamma function.
Abstract: This paper presents some inequalities concerning certain ratios of the classical Euler’s Gamma function. The results generalized some recent results.
5 citations
TL;DR: In this paper, the author analyzes the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, including the ratio of two q-Gamma functions.
Abstract: In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio of two gamma functions and divided differences of polygamma functions, and related monotonicity results.
TL;DR: The q-analogue of Gamma function (orq-deformed Gamma function) was introduced by Thomae [17] and later by Jackson [5, 6] as the infinite product as mentioned in this paper.
Abstract: . In this paper, we rederive the identity Γ q (x)Γ q (1 −x) = π q sin q (π q x) . Then, we give q-analogue of Gauss’ multiplication formulaand study representation of q-oscillator algebra in terms of the q-factorialpolynomials. 1. IntroductionIn the last decades, the q-calculus served as a bridge between mathematicsand physics. The majority of researchers around the world who use q-calculusare physicists. This field has expanded explosively, due to the fact that thebasic hypergeometric series served several subjects of combinatorics, quantumtheory, number theory, statistical mechanics.From now on we will restrict our concern to the case that the deformationparameter qis real and 0