Showing papers on "q-gamma function published in 2016"
13 Feb 2016
TL;DR: In this paper, the authors study the applicability of the extension of quantum calculus based on two parameters and propose the $(p,q)$-Durrmeyer operators, estimate moments and establish some direct results.
Abstract: In the present paper, we study the applications of the extension of quantum calculus based on two parameters. We define beta function and establish an identity with gamma function, for two parameters $(p,q)$, i e. the post-quantum calculus. We also propose the $(p,q)$-Durrmeyer operators, estimate moments and establish some direct results. Depending on the selection of $p$ and $q,$ the rate of convergence of the our new operators can provide better approximation than those of the Bernstein-Durrmeyer operators and its $q$-analogue. In the end, we provide some graphs using the software Mathematica.
35 citations
1 Dec 2016
TL;DR: In this paper, the authors propose the $(p,q)$-variant of the beta function of second kind and establish a relation between the generalized beta and gamma functions using some identities of the post-quantum calculus.
Abstract: In the present article, we propose the $(p,q)$-variant of beta function of second kind and establish a relation between the generalized beta and gamma functions using some identities of the post-quantum calculus. As an application, we also propose the $(p,q)$-Baskakov-Durrmeyer operators, estimate moments and establish some direct results.
22 citations
TL;DR: In this paper, the monotonicity property for two functions involving the logarithmic of the q-gamma function is proven for all q > 0, where q is a constant.
Abstract: In this paper, the monotonicity property for two functions involving the logarithmic of the q-gamma function is proven for all \(q>0\). As a consequence, sharp inequalities for the q-gamma function are established. Our results are shown to be as a generalization of results which were obtained by Anderson and Qiu (Proc Am Math Soc 125:3355–3362, 1997).
12 citations
TL;DR: In this article, the authors presented the Raabe integral and Hermite's formula for q -gamma function Γq(x), 0 < q < 1, and deduced new proofs of the formulas Γ′q (x) Γ q(x), and q -Gauss multiplication using the Hermite formula of Γqs and H. Jack's technique.
Abstract: In this paper, we presented the Raabe’s integral and Hermite’s formula for q -gamma function Γq(x) , 0 < q < 1 . We deduced new proofs of the formulas Γ′q(x) Γq(x) and q -Gauss’s multiplication using the Hermite’s formula of Γq(x) and H. Jack’s technique [11]. Also, we deduced new double inequality of Γq(x) . Mathematics subject classification (2010): 33D05, 26D07, 65Q20.
5 citations
TL;DR: In this paper, the authors determined the radius of starlikeness of the functions in function series and the convexity of the function for a function q in [{1}/{\sqrt{e}},1] for the case q = q ∈ [{ 1}/{e, 1].
Abstract: In this paper, we determine the radius of starlikeness of \(\Gamma _q\) and \(1/\Gamma _q\) and the radius of convexity of the function \(1/\Gamma _q\) for \(q\in [{1}/{\sqrt{e}},1)\). The basic tools of our work are the developments of the functions in function series.
1 citations
1 Oct 2016
TL;DR: In this paper, the q- analogue of the incomplete gamma function and its first derivative for all real numbers were obtained using neutrix calculus, and the first derivative of the gamma function was shown to be a function of real numbers.
Abstract: In this paper, we use neutrix calculus in order to obtain some results on the q- analogue of the incomplete gamma function and its first derivative for all real numbers