Related papers: Some Appell-type orthogonal polynomials on lattice…
In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the \textit{standard} $q$-Racah polynomials are introduced. Several algebraic properties of these polynomials are obtained and…
This article considers some q-analogues of classical results concerning the Ehrhart polynomials of Gorenstein polytopes, namely properties of their q-Ehrhart polynomial with respect to a good linear form. Another theme is a specific linear…
This paper addresses a construction of new $q-$Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order…
In this paper the general Krall-type Askey-Wilson polynomials are introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points $\pm1$. Several…
We study matrix elements of a change of base between two different bases of representations of the quantum algebra $U_q(su(1,1))$. The two bases, which are multivariate versions of Al-Salam--Chihara polynomials, are eigenfunctions of…
The classical q-hypergeometric orthogonal polynomials are assembled into a hierarchy called the q-Askey scheme. At the top of the hierarchy, there are two closely related families, the Askey-Wilson and q-Racah polynomials. As it is well…
We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in \cite{Kusa} actually characterize them. Secondly, by…
Inspired by Aomoto's $q$-Selberg integral, the orthogonal ensemble in the exponential lattice is considered in this paper. By introducing a skew symmetric kernel, the configuration space of this ensemble is constructed to be symmetric and…
An analogue of Taylor's formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. We study the convergence of the associated Taylor series. Our results…
A special Infeld-Hall factorization is given for the Askey-Wilson second order q-difference operator. It is then shown how to deducd a generalization of the corresponding Askey-Wilson polynomials.
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi…
In this paper we introduce and discuss some classes of orthogonal polynomials in several non-commuting variables. The emphasis is on a non-commutative version of the orthogonal polynomials on the real line. We introduce recurrence equations…
The exceptional Racah and q-Racah polynomials are constructed. Together with the exceptional Laguerre, Jacobi, Wilson and Askey-Wilson polynomials discovered by the present authors in 2009, they exhaust the generic exceptional orthogonal…
In this contribution, discrete semiclassical orthogonal polynomials of class $s\leq2$ are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class. We also consider limit…
We prove that for |x|,|t|<1, -1 <q \leq1 and n\geq0: \Sigma_{i\geq0}((t^{i})/((q)_{i}))h_{n+i}(x|q) = h_{n}(x|t,q) \Sigma_{i\geq0}((t^{i})/((q)_{i}))h_{i}(x|q), where h_{n}(x|q) and h_{n}(x|t,q) are respectively the so called q-Hermite and…
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous…
Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite…
We introduce and study symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic lattice models with $\Delta=\pm 1/2$. There is also a close relation to…
An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to…