Related papers: Discrete q-Hermite polynomials: An elementary appr…
We use generating functions to express orthogonality relations in the form of $q$-beta integrals. The integrand of such a $q$-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal
We investigate on some Appel-type orthogonal polynomial sequences on q-quadratic lattices and we provide some entire new characterizations of the Al-Salam Chihara polynomials (including the Rogers q-Hermite polynomials). The corresponding…
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
We solve the connection coefficient problem between the Al-Salam-Chihara polynomials and the q-Hermite polynomials, and we use the resulting identity to answer a question from probability theory. We also derive the distribution of some…
The purpose of this article is to present, in a simple way, an analytic approach to special numbers and polynomials. The approach is based on the derivative polynomials. The paper is, to some extent, a review article, although it contains…
It is shown that some q-analogues of the Fibonacci and Lucas polynomials lead to q-analogues of the Chebyshev polynomials which retain most of their elementary properties.
We give simple proofs for the Hankel determinants of q-exponential polynomials.
Using a realization of the q-exponential function as an infinite multiplicative sereis of the ordinary exponential functions we obtain new nonlinear connection formulae of the q-orthogonal polynomials such as q-Hermite, q-Laguerre and…
The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…
The q-Hermite I-Sobolev type polynomials of higher order are consider for their study. Their hypergeometric representation is provided together with further useful properties such as several structure relations which give rise to a…
We use the Legendre polynomials and the Hermite polynomials as two examples to illustrate a simple and systematic technique on deriving asymptotic formulas for orthogonal polynomials via recurrence relations. Another application of this…
In this paper, we study some properties of the q-Appell polynomials, including the recurrence relations and the q-difference equations which extend some known calssical (q=1) results. We also provide the recurrence relations and the…
This research is aimed to give a determinantal definition for the $q$-Appell polynomials and show some classical properties as well as find some interesting properties of the mentioned polynomials in the light of the new definition.
We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…
We obtain weight functions associated with $q$-linear and $q$-quadratic lattices that yield discrete orthogonality with respect to a quasi-definite moment functional for the Askey-Wilson polynomials and all the polynomial sequences in the…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
We introduce polynomial sets of $(p,q)$-Appell type and give some of their characterizations. The algebraic properties of the set of all polynomial sequences of $(p,q)$-Appell type are studied. Next, we give a recurrence relation and a…
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
Orthogonal q-polynomials associated with q-Laguerre-Hahn form will be studied as a generalization of the q-semiclassical forms via a suitable q-difference equation. The concept of class and a criterion to determinate it will be given. The…
We introduce degenerate Hermite polynomials as a degenerate version of the ordinary Hermite polynomials. Then, among other things, by using the formula about representing one lambda-Sheffer polynomial in terms of other lambda-Sheffer…