Showing papers on "q-gamma function published in 2017"
TL;DR: In this paper, a (p, q)-Szász-Durrmeyer operator is proposed to estimate moments and establish direct results of the Gamma function, which is based on the (n, q) analogue of Gamma function.
Abstract: We define a (p, q) analogue of Gamma function. As an application, we propose (p, q)-Szász–Durrmeyer operators, estimate moments and establish some direct results.
23 citations
7 citations
TL;DR: In this paper, two classes of completely monotonic functions involving the gamma function are investigated and exploited to establish sharp inequalities for the gamma and the digamma functions, and these results extend to the q-gamma function for all q>0.
Abstract: In this paper, two classes of completely monotonic functions involving the gamma function are investigated and exploited to establish sharp inequalities for the gamma and the digamma functions. These results extend to the q-gamma function for all \(q>0\). Sharp bounds for the q-gamma and the q-digamma functions are provided in terms of the inverse hyperbolic function (arcsinh).
7 citations
TL;DR: In this article, the logarithmically complete monotonicity property for a function involving a q-gamma function is investigated for q = q ∈ (0, 1).
Abstract: In this paper, the logarithmically complete monotonicity property for a functions involving q-gamma function is investigated for $$q\in (0,1).$$
As applications of this results, some new inequalities for the q-gamma function are established. Furthermore, let the sequence $$r_n$$
be defined by $$n!=\sqrt{2\pi n}(n/e)^n e^{r_n}$$
. We establish new estimates for Stirling’s formula remainder $$r_n.$$
4 citations
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TL;DR: In this article, the authors considered a family of solutions of the Riccati equation and proved that the meromorphic solutions of these solutions are concerning with the $q-gamma function.
Abstract: We consider a family of solutions of $q-$difference Riccati equation, and prove the meromorphic solutions of $q-$difference Riccati equation and corresponding second order $q-$difference equation are concerning with $q-$gamma function. The growth and value distribution of differences on solutions of $q-$difference Riccati equation are also investigated.
1 citations
TL;DR: In this paper, the authors obtained limit formulas for derivatives of (p, q)-gamma function and digamma function at the poles of the Prabhu-Srivastava theorem.
Abstract: In this paper, we obtain some limit formulas for derivatives of (p,q)-gamma function and (p,q)-digamma function at their poles. These limit formulas extend the Prabhu-Srivastava theorem involving gamma function and digamma function.
1 citations
TL;DR: In this article, Baliarsingh et al. introduced the concepts of statistically weighted Ψ Δ p, q -summability, weighted Ω Δ p, q -statistical convergence and weighted strongly ΩΩ Δ q, q −summabilities with respect to the difference operator Δ h, p, Q α, β, γ including ( p, Q ) -analogue of Gamma function and proved a Korovkin type approximation theorem for functions of two variables.