Orthogonal polynomials on a bi-lattice
Classical Analysis and ODEs
2015-03-17 v1
Abstract
We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-\beta. We combine both lattices to obtain the bi-lattice N \cup (N+1-\beta) and show that the orthogonal polynomials on this bi-lattice have recurrence coefficients which satisfy a non-linear system of recurrence equations, which we can identify as a limiting case of an (asymmetric) discrete Painlev\'e equation.
Cite
@article{arxiv.1101.1817,
title = {Orthogonal polynomials on a bi-lattice},
author = {Christophe Smet and Walter Van Assche},
journal= {arXiv preprint arXiv:1101.1817},
year = {2015}
}
Comments
25 pages, 2 figures