Linear partial \(q\)-difference equations on \(q\)-linear lattices and their bivariate \(q\)-orthogonal polynomial solutions

DOI10.1016/j.amc.2013.08.018zbMath1329.39011arXiv1305.3819OpenAlexW1986563468MaRDI QIDQ907574

N. E. Zubov

Publication date: 25 January 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.3819

zbMATH Keywords

\(q\)-integral\(q\)-derivative operator\(q\)-Pearson systembivariate \(q\)-orthogonal polynomialsbivariate big \(q\)-Jacobi polynomialsgeneralized bivariate basic hypergeometric seriespartial \(q\)-difference equations

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Difference equations, scaling ((q)-differences) (39A13)

Related Items (12)

Monic bivariate polynomials on quadratic and \(q\)-quadratic lattices ⋮ On a symmetric generalization of bivariate Sturm-Liouville problems ⋮ Zero sets of bivariate Hermite polynomials ⋮ Linear Partial Divided-Difference Equation Satisfied by Multivariate Orthogonal Polynomials on Quadratic Lattices ⋮ Bivariate Symmetric Discrete Orthogonal Polynomials ⋮ Impulsive antiperiodic boundary value problems for nonlinear \(q_k\)-difference equations ⋮ Hypergeometric Multivariate Orthogonal Polynomials ⋮ Impulsive fractional \(q\)-integro-difference equations with separated boundary conditions ⋮ Successive iteration and positive extremal solutions for nonlinear impulsive \(q_{k}\)-difference equations ⋮ Scattering theory of impulsive Sturm-Liouville equation in quantum calculus ⋮ Fixed point theory approach to boundary value problems for second-order difference equations on non-uniform lattices ⋮ ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS

Uses Software

• DLMF

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