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The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation

Clarkson, Peter, Jordaan, Kerstin (2014) The Relationship Between Semiclassical Laguerre Polynomials and the Fourth Painlevé Equation. Constructive Approximation, 39 (1). pp. 223-254. ISSN 0176-4276. (doi:10.1007/s00365-013-9220-4) (KAR id:51256)

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Official URL
http://dx.doi.org/10.1007/s00365-013-9220-4

Abstract

We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semiclassical Laguerre weight and classical solutions of the fourth Painlevé equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions that arise in the description of special function solutions of the fourth Painlevé equation.

Item Type: Article
DOI/Identification number: 10.1007/s00365-013-9220-4
Uncontrolled keywords: Semiclassical orthogonal polynomials; Recurrence coefficients; Painless equations; Wronskians; Parabolic cylinder functions; Hamiltonians
Subjects: Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Peter Clarkson
Date Deposited: 29 Oct 2015 09:25 UTC
Last Modified: 16 Feb 2021 13:29 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51256 (The current URI for this page, for reference purposes)
Clarkson, Peter: https://orcid.org/0000-0002-8777-5284
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