Plancherel_Rotach Asymptotics for q-Orthogonal Polynomials
Classical Analysis and ODEs
2012-06-22 v1
Abstract
We establish the Plancherel-Rotach-type asymptotics around the largest zero (the soft edge asymptotics) for some classes of polynomials satisfying three-term recurrence relations with exponentially increasing coefficients. As special cases, our results include this type of asymptotics for q^{-1}-Hermite polynomials of Askey, Ismail and Masson, q-Laguerre polynomials, and the Stieltjes-Wigert polynomials. We also introduce a one parameter family of solutions to the q-difference equation of the Ramanujan function.
Cite
@article{arxiv.1206.4737,
title = {Plancherel_Rotach Asymptotics for q-Orthogonal Polynomials},
author = {Mourad E. H. Ismail and Xin Li},
journal= {arXiv preprint arXiv:1206.4737},
year = {2012}
}
Comments
16 pages