Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations
Identificadores
URI: https://hdl.handle.net/10481/77095Metadata
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Taylor & Francis
Materia
Bivariate orthogonal polynomials Freud orthogonal polynomials Three term relations Matrix Painlevé-type difference equations
Date
2022-08-22Referencia bibliográfica
Published version: Cleonice F. Bracciali, Glalco S. Costa & Teresa E. Pérez (2022) Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations, Journal of Difference Equations and Applications, DOI: [10.1080/10236198.2022.2119140]
Sponsorship
Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) 88887.310463/2018-00 88887.575407/2020-00; FEDER/Junta de Andalucia A-FQM-246-UGR20; MCIN PGC2018-094932B-I00; European Commission; IMAG-Maria de Maeztu grant CEX2020-00 1105-MAbstract
We study bivariate orthogonal polynomials associated with Freud
weight functions depending on real parameters. We analyse 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 differentialdifference
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.