Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic Cylinder Functions

Autor:	Finster, Felix, Smoller, Joel
Rok vydání:	2012
Předmět:	Mathematics - Classical Analysis and ODEs Mathematical Physics
Zdroj:	Commun. Math. Sci. 12 (2014) 175-200
Druh dokumentu:	Working Paper
DOI:	10.4310/CMS.2014.v12.n1.a8
Popis:	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. Comment: 25 pages, LaTeX, 7 figures (published version)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1207.6861 Zobrazit plný text záznamu View this record from Arxiv