Recurrence coefficients for discrete orthonormal polynomials and the Painlev\'e equations
Exactly Solvable and Integrable Systems
2013-07-19 v3 Classical Analysis and ODEs
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 Painlev\'e equations.
Cite
@article{arxiv.1301.2396,
title = {Recurrence coefficients for discrete orthonormal polynomials and the Painlev\'e equations},
author = {Peter A Clarkson},
journal= {arXiv preprint arXiv:1301.2396},
year = {2013}
}
Comments
21 pages, some revisions made