Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic Cylinder Functions
Classical Analysis and ODEs
2013-09-10 v3 Mathematical Physics
math.MP
Abstract
We derive WKB approximations for a class of Airy and parabolic cylinder functions in the complex plane, including quantitative error bounds. We prove that all zeros of the Airy function lie on a ray in the complex plane, and that the parabolic cylinder functions have no zeros. We also analyze the Airy and Airy-WKB limit of the parabolic cylinder functions.
Keywords
Cite
@article{arxiv.1207.6861,
title = {Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic Cylinder Functions},
author = {Felix Finster and Joel Smoller},
journal= {arXiv preprint arXiv:1207.6861},
year = {2013}
}
Comments
25 pages, LaTeX, 7 figures (published version)