Related papers: Constant coefficient Laurent biorthogonal polynomi…
The main objects of the investigation presented in this paper are branched-continued-fraction representations of ratios of contiguous hypergeometric series and type II multiple orthogonal polynomials on the step-line with respect to linear…
We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the…
An ordering for Laurent polynomials in the algebraic torus $(\mathbb C^*)^D$, inspired by the Cantero-Moral-Vel\'azquez approach to orthogonal Laurent polynomials in the unit circle, leads to the construction of a moment matrix for a given…
We establish some new Tur\'an's type inequalities for orthogonal polynomials defined by a three-term recurrence with monotonic coefficients. As a corollary we deduce asymptotic bounds on the extreme zeros of orthogonal polynomials with…
A new set of finite 2D biorthogonal polynomials is defined using the finite orthogonal polynomials $N_{n}^{(p)}(w)$ and the Konhauser polynomials. We present a connection between this finite 2D biorthogonal set and the generalized…
Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of ($q=1$) classical orthogonal polynomials, and study those cases in which the…
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…
We study the Dickson polynomials of the (k+1)-th kind over the field of complex numbers. We show that they are a family of co-recursive orthogonal polynomials with respect to a quasi-definite moment functional L_{k}. We find an integral…
We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study…
We prove that the constant terms of powers of a Laurent polynomial satisfy certain congruences modulo prime powers. As a corollary, the generating series of these numbers considered as a function of a p-adic variable satisfies a non-trivial…
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…
In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a…
Given $\{P_n \}$ a sequence of monic orthogonal polynomials, we analyze their linear combinations $\{Q_n \}$with constant coefficients and fixed length $k+1$. Necessary and sufficient conditions are given for the orthogonality of the monic…
Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain $q$-analogues of Laguerre and Charlier polynomials. The moments of these orthogonal polynomials have combinatorial models in terms of crossings in permutations and set…
This paper provides a finite pair of biorthogonal matrix polynomials and their finite biorthogonality, several recurrence relations, matrix differential equation, generating function and integral representation.
We show that the Lagrange interpolation polynomials are biorthogonal with respect to a set of rational functions whose poles coinicde with interpolation points
We study the higher-order Euler polynomials and give the corresponding monic orthogonal polynomials, which are Meixner-Pollaczek polynomials with certain arguments and constant factors. Moreover, through a general connection between moments…
In this paper, we construct the pair of finite bivariate biorthogonal M-Konhauser polynomials, reduced to the finite orthogonal polynomials $M_{n}^{(p,q)}(t)$, by choosing appropriate parameters in order to obtain a relation between the…
We consider orthogonal polynomials p_n with respect to an exponential weight function w(x) = exp(-P(x)). The related equations for the recurrence coefficients have been explored by many people, starting essentially with Laguerre [49], in…
We obtain factorial moment identities for the Charlier, Meixner and Krawtchouk orthogonal polynomial ensembles. Building on earlier results by Ledoux [Elect. J. Probab. 10, (2005)], we find hypergeometric representations for the factorial…