Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations

Clarkson, Peter (2013) Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations. Journal of Physics A: Mathematical and Theoretical, 46 (18). ISSN 1751-8113. (doi:10.1088/1751-8113/46/18/185205)

Abstract

We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations can be expressed in terms of Wronskians of modified Bessel functions and confluent hypergeometric functions, respectively for the generalized Charlier and generalized Meixner polynomials. These Wronskians arise in the description of special function solutions of the third and fifth Painlevé equations.

Item Type: Article
DOI/Identification number: 10.1088/1751-8113/46/18/185205
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: 30 Jan 2013 18:55 UTC
Last Modified: 29 May 2019 09:59 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/33120 (The current URI for this page, for reference purposes)
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