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)

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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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Peter A Clarkson
Date Deposited: 29 Oct 2015 09:25 UTC
Last Modified: 29 May 2019 16:13 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51256 (The current URI for this page, for reference purposes)
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