Two variable Freud orthogonal polynomials and matrix Painlev\'e-type difference equations
Classical Analysis and ODEs
2022-08-23 v1
Abstract
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 coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differential-difference equation for the bivariate orthogonal polynomials is deduced. The extension of the Painlev\'e equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained.
Cite
@article{arxiv.2208.10361,
title = {Two variable Freud orthogonal polynomials and matrix Painlev\'e-type difference equations},
author = {Cleonice F. Bracciali and Glalco S. Costa and Teresa E. Pérez},
journal= {arXiv preprint arXiv:2208.10361},
year = {2022}
}
Comments
18 pages, accepted for publication by Journal of Difference Equations and Applications