Two variable Freud orthogonal polynomials and matrix Painlev\'e-type difference equations

Autor:	Bracciali, Cleonice F., Costa, Glalco S., Pérez, Teresa E.
Rok vydání:	2022
Předmět:	Mathematics - Classical Analysis and ODEs 42C05 33C50
Druh dokumentu:	Working Paper
Popis:	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. Comment: 18 pages, accepted for publication by Journal of Difference Equations and Applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.10361 Zobrazit plný text záznamu View this record from Arxiv