Related papers: Une $q$-d\'eformation de la transformation de Barg…

In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.

We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.

I present a $q$-analog of the discrete Painlev\'e I equation, and a special realization of it in terms of $q$-orthogonal polynomials.

We introduce four q-analogs of the double Laplace transform and prove some of their main properties. Next we show how they can be used to solve some q-functional equations and partial q-differential equations.

We give a q-analogue of Gauss' divisibility theorem

We combine continuous $q^{-1}$-Hermite Askey polynomials with new $2D$ orthogonal polynomials introduced by Ismail and Zhang as $q$-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative…

In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…

A q-version of the Fourier transformation and some of its properties are discussed.

Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.

This note gives a simple approach to q-analogues of some results associated with Abel polynomials.

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…

The article deals with q-analogs of the three- and four-dimensional Euclidean superalgebra and the Poincare superalgebra.

We characterize of the $q$-Bernstein functions in terms of $q$-Laplace transform. Moreover, we present several results of $q$-completely monotonic, $q$-log completely monotonic and $q$-Bernstein functions.

We reconsider the Bargmann-Dirichlet space on the complex plane $\mathbb{C}$ and its generalizations considered in [8]. Concretely, we first present a new characterization of such spaces as harmonic spaces of the magnetic Laplacian with…

We present a multivariable generalization of the digital binomial theorem from which a q-analog is derived as a special case.

We introduce a Bargmann transform on the space of hyperplanes by applying the Plancherel formula of the Radon transform to the definition of the Bargmann transform on the Euclidean space. Some basic facts on microlocal analysis are also…

We give an overview about the power product expansion of the exponential series and derive some q-analogs

Let $\mu_p^{(q)}$ be the q-deformed Poisson measure in the sense of Saitoh Yoshida and $\nu_p$ be the measure given by Equation \eqref{eq:nu-q}. In this short paper, we introduce the q-deformed analogue of the Segal-Bargmann transform…

We study some q-analogues of the Racah polynomials and some of their applications in the theory of representation of quantum algebras.