Related papers: Connection coefficients for classical orthogonal p…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
Classical orthogonal polynomials have widespread applications including in numerical integration, solving differential equations, and interpolation. Changing basis between classical orthogonal polynomials can affect the convergence,…
Hahn polynomials of several variables can be defined by using the Jacobi polynomials on the simplex as a generating function. Starting from this connection, a number of properties for these two families of orthogonal polynomials are…
We describe fast algorithms for approximating the connection coefficients between a family of orthogonal polynomials and another family with a polynomially or rationally modified measure. The connection coefficients are computed via…
The connection between the recoupling scheme of four copies of $\mathfrak{su}(1,1)$, the generic superintegrable system on the 3 sphere, and bivariate Racah polynomials is identified. The Racah polynomials are presented as connection…
Let $d\nu$ be a measure in $\mathbb{R}^d$ obtained from adding a set of mass points to another measure $d\mu$. Orthogonal polynomials in several variables associated with $d\nu$ can be explicitly expressed in terms of orthogonal polynomials…
In this paper we investigate the multivariate orthogonal polynomials based on the theory of interacting Fock spaces. Our framework is on the same stream line of the recent paper by Accardi, Barhoumi, and Dhahri \cite{ABD}. The (classical)…
In this paper, a fourth-order partial divided-difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this equation we obtain explicitly the matrix coefficients…
In this paper, we study a class of orthogonal polynomials defined by a three-term recurrence relation with periodic coefficients. We derive explicit formulas for the generating function, the associated continued fraction, the orthogonality…
We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form $y^m = \phi(x)$ in $\mathbb{R}^2$ where $m = 1, 2$ and $\phi$ is a polynomial of arbitrary degree $d$, in terms of univariate semiclassical OPs. We compute…
A correlation function of the classical orthogonal polynomials is defined and determined. The correlation function obeys a second order difference equation in two variables. The correlation function for the Gegenbauer, Chebyshev and…
Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We…
The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is seen to admit as subalgebras Racah and Jacobi algebras of…
This article is devoted to the computation of Jack connection coefficients, a generalization of the connection coefficients of two classical commutative subalgebras of the group algebra of the symmetric group: the class algebra and the…
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…
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 Gasper and Rahman multivariate $(-q)$-Racah polynomials appear as connection coefficients between bases diagonalizing different abelian subalgebras of the recently defined higher rank $q$-Bannai-Ito algebra $\mathcal{A}_n^q$. Lifting…
This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic…
It has been known since 2007 that the Wilson and Racah polynomials can be characterized as basis functions for irreducible representations of the quadratic symmetry algebra of the quantum superintegrable system on the 2-sphere,…
Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these…