Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems
Classical Analysis and ODEs
2013-10-11 v3
Abstract
We study the Plancherel--Rotach asymptotics of four families of orthogonal polynomials, the Chen--Ismail polynomials, the Berg-Letessier-Valent polynomials, the Conrad--Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.
Cite
@article{arxiv.1302.6196,
title = {Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems},
author = {Dan Dai and Mourad E. H. Ismail and Xiang-Sheng Wang},
journal= {arXiv preprint arXiv:1302.6196},
year = {2013}
}
Comments
34 pages, typos corrected and references updated