Title: The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
Authors: Filipuk, Galina ×
Van Assche, Walter
Zhang, Lun #
Issue Date: May-2012
Publisher: Institute of Physics Publishing
Series Title: Journal of Physics A, Mathematical and Theoretical vol:45 issue:20 pages:205201-(13 pp)
Abstract: We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlevé equation when viewed as functions of one of the parameters in the weight. We compare different approaches to derive this result, namely, the ladder operators approach, the isomonodromy deformations approach and combining the Toda system for the recurrence coefficients with a discrete equation. We also discuss a relation between the recurrence coefficients for the Freud weight and the semi-classical Laguerre weight and show how it arises from the Bäcklund transformation of the fourth Painlevé equation.
ISSN: 1751-8113
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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