# The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation

Clarkson, Peter, Jordaan, Kerstin (2014) The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation. Constructive Approximation, 39 (1). pp. 223-254. ISSN 0176-4276. (doi: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 10.1007/s00365-013-9220-4 Q Science > QA Mathematics (inc Computing science) > QA351 Special functionsQ Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics Peter A Clarkson 30 Jan 2013 18:46 UTC 01 Aug 2019 10:35 UTC https://kar.kent.ac.uk/id/eprint/33119 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-8777-5284