Multiple orthogonal polynomials associated with an exponential cubic weight
Classical Analysis and ODEs
2015-02-05 v2
Abstract
We consider multiple orthogonal polynomials associated with the exponential cubic weight e^{-x^3} over two contours in the complex plane. We study the basic properties of these polynomials, including the Rodrigues formula and nearest-neighbor recurrence relations. It turns out that the recurrence coefficients are related to a discrete Painlev\'e equation. The asymptotics of the recurrence coefficients, the ratio of the diagonal multiple orthogonal polynomials and the (scaled) zeros of these polynomials are also investigated.
Cite
@article{arxiv.1306.3835,
title = {Multiple orthogonal polynomials associated with an exponential cubic weight},
author = {Walter Van Assche and Galina Filipuk and Lun Zhang},
journal= {arXiv preprint arXiv:1306.3835},
year = {2015}
}
Comments
23 pages, 7 figures