A characterization of the Rogers -Hermite polynomials.
A note on the Rogers-Fine identity.
An embedding norm and the Lindqvist trigonometric functions.
Expectation of Random Polytopes.
Generalization of some inequalities for the -gamma function.
Hypergeometric -functions of the -Painlevé system of type .
Hypergeometric functions of the -Painlevé systems of type .
Inequalities for Taylor series involving the divisor function
Let where denotes the number of positive divisors of the natural number . We present monotonicity properties of functions defined in terms of . More specifically, we prove that is strictly increasing on , while is strictly decreasing on . These results are then applied to obtain various inequalities, one of which states that the double inequality holds with the best possible constant factors and . Here, denotes Euler’s constant. This refines a result of Salem, who proved the inequalities...
Mean Value Theorems in q-calculus
New inequalities for some special and -special functions.
On another extension of -Pfaff-Saalschütz formula
In this paper we give an extension of -Pfaff-Saalschütz formula by means of Andrews-Askey integral. Applications of the extension are also given, which include an extension of -Chu-Vandermonde convolution formula and some other -identities.
On integral representations of -gamma and -beta functions
We study -integral representations of the -gamma and the -beta functions. As an application of these integral representations, we obtain a simple conceptual proof of a family of identities for Jacobi triple product, including Jacobi's identity, and of Ramanujan's formula for the bilateral hypergeometric series.
On -summation and confluence
This paper is divided in two parts. In the first part we study a convergent -analog of the divergent Euler series, with , and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding -difference equation. In the second part, we work under the assumption . In this case, at least four different -Borel sums of a divergent power series solution of an irregular singular...
On some Feng Qi type -integral inequalities.
On some Feng Qi type -integral inequalities.
On the -analogue of gamma functions and related inequalities.
Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus
Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs...
Some inequalities for the -digamma function.
Some new Formulas involving Functions
The multiple gamma function and its q-analogue
We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vignéras multiple gamma function by considering the classical limit of the multiple q-gamma function.