Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials

We consider two semiclassical extensions of the Laguerre weight and their associated sets of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the coefficients appearing in this relation satisfy discrete Painlevé equations.

Saved in:
Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2010-04, Vol.138 (4), p.1317-1331
Main Authors: BOELEN, LIES, VAN ASSCHE, WALTER
Format: Article
Language:English
Subjects:
Coefficients
Difference and functional equations, recurrence relations
Difference equations
Exact sciences and technology
General mathematics
General, history and biography
Integrating factors
Mathematical analysis
Mathematical expressions
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Polynomials
Real lines
Recurrence relations
Research grants
Sciences and techniques of general use
Special functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider two semiclassical extensions of the Laguerre weight and their associated sets of orthogonal polynomials. These polynomials satisfy a three-term recurrence relation. We show that the coefficients appearing in this relation satisfy discrete Painlevé equations.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-09-10152-1