Journal
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
Volume 28, Issue 9, Pages 1157-1177Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10236198.2022.2119140
Keywords
Bivariate orthogonal polynomials; Freud orthogonal polynomials; three term relations; matrix Painleve-type difference equations
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Funding
- Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) [88887.310463/2018-00, 88887.575407/2020-00]
- FEDER/Junta de Andalucia [A-FQM-246-UGR20]
- MCIN [PGC2018-094932B-I00]
- FEDER
- IMAG-Maria de Maeztu grant [CEX2020-00 1105-M]
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This paper studies bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. The relationships between the matrix coefficients of the three term relations for the orthonormal polynomials and the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials are analyzed. A matrix differential-difference equation for the bivariate orthogonal polynomials is also derived. The extension of the Painleve equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained.
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 differential-difference equation for the bivariate orthogonal polynomials is deduced. The extension of the Painleve equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained.
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