Linear Partial Divided-Difference Equation Satisfied by Multivariate Orthogonal Polynomials on Quadratic Lattices

DOI10.1051/mmnp/201712303zbMath1384.33023arXiv1605.09280OpenAlexW3048848007MaRDI QIDQ4607551

No author found.

Publication date: 14 March 2018

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09280

zbMATH Keywords

partial difference equationquadratic latticenonuniform latticebivariate Racah polynomialspartial divided-difference equationbivariate Wilson polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50) Partial difference equations (39A14) Numerical methods for difference equations (65Q10)

Related Items

Monic bivariate polynomials on quadratic and \(q\)-quadratic lattices, On moments of hypergeometric bivariate weight functions, Preface for the Special Issue on “Special functions and analysis of PDEs”, Hypergeometric Multivariate Orthogonal Polynomials

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On solutions of holonomic divided-difference equations on nonuniform lattices
• Multivariable Askey-Wilson function and bispectrality
• Bivariate second-order linear partial differential equations and orthogonal polynomial solutions
• On a class of bivariate second-order linear partial difference equations and their monic orthogonal polynomial solutions
• Racah polynomials and recoupling schemes of \(\mathfrak{su}(1,1)\)
• Linear partial \(q\)-difference equations on \(q\)-linear lattices and their bivariate \(q\)-orthogonal polynomial solutions
• Two-variable orthogonal polynomials of big \(q\)-Jacobi type
• On classical orthogonal polynomials
• Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points
• Some combinatorial and analytical identities
• Multivariable \(q\)-Racah polynomials
• Structure relations for the bivariate big \(q\)-Jacobi polynomials
• On structure formulas for Wilson polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• A Whipple’s Transformation for Hypergeometric Series in $U(n)$ and Multivariable Hypergeometric Orthogonal Polynomials
• Some Hypergeometric Orthogonal Polynomials
• Some multivariable orthogonal polynomials of the Askey tableau—Continuous families
• Some multivariable orthogonal polynomials of the Askey tableau-discrete families
• On difference equations for orthogonal polynomials on nonuniform lattices¹