The relationship between semi-classical Laguerre polynomials and the fourth Painlev\'e equation
Exactly Solvable and Integrable Systems
2017-11-07 v4 Classical Analysis and ODEs
Abstract
We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semi-classical Laguerre weight and classical solutions of the fourth Painlev\'e equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions which arise in the description of special function solutions of the fourth Painlev\'e equation.
Cite
@article{arxiv.1301.4134,
title = {The relationship between semi-classical Laguerre polynomials and the fourth Painlev\'e equation},
author = {Peter A. Clarkson and Kerstin Jordaan},
journal= {arXiv preprint arXiv:1301.4134},
year = {2017}
}
Comments
23 pages