Showing papers on "q-gamma function published in 2018"
TL;DR: In this paper, the reciprocity theorem for q-gamma functions involving two and more variables was proved and generalized to several variables by Berndt and Koukoulopoulos (Proc Am Math Soc 601:2369-2373, 2007).
Abstract: In one of his notebooks, Ramanujan stated but did not prove an identity for a ratio of gamma functions involving two separate variables. Such an identity was referred to as a reciprocity theorem due to the symmetry relations between the variables. The two variable result was later proved and generalized to several variables by Berndt and Koukoulopoulos (Proc Am Math Soc 601:2369–2373, 2007). In this paper, we state and prove similar reciprocity theorems for ratios of q-gamma functions involving two and more variables.
1 citations
TL;DR: In this article, a characterisation of the symmetric q-Gamma function is given, and some special q-calculus technics are used to obtain the characterizations.
Abstract: In this work we are interested by giving new characterizations of the symmetric q-Gamma function and show that there are intimately related. For that, some special q-calculus technics are used.
1 citations
Journal Article•
TL;DR: In this paper, the complete monotonicity property for functions related to the $q$-gamma and the polygamma functions was proved and exploited to establish some inequalities.
Abstract: In this paper, the complete monotonicity property for functions related to the $q$-gamma and the $q$-polygamma functions, where $q$ is a positive real number, is proved and exploited to establish some inequalities for the $q$-gamma and the $q$-polygamma functions.
1 citations
TL;DR: In this paper, the authors investigated a certain type of q-difference Riccati equation in the complex plane and proved that it possesses a one parameter family of meromorphic solutions.
Abstract: In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and q ∈ C such that 0 < |q| < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.
1 citations
Posted Content•
TL;DR: This paper deduced some relations for the q-Pochhammer symbol, q-binomial coefficient, Q-bracket, qfactorial, and q-Gamma function.
Abstract: I deduce some relations for the q-Pochhammer symbol, the q-binomial coefficient, the q-bracket, the q-factorial and the q-Gamma function.
TL;DR: In this paper, an inequality involving the q-gamma and q-trigamma functions is derived and proved for all real number values q > 0, where q is a real number.
Abstract: An inequality involving the q-gamma and q-trigamma functions is derived and proved for all real number $$q>0$$
. This inequality provides new bounds for the q-gamma function in terms of the q-trigamma function.