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Absence of zeros and asymptotic error estimates for Airy and parabolic cylinder functions

Finster, Felix and Smoller, Joel (2012) Absence of zeros and asymptotic error estimates for Airy and parabolic cylinder functions. Preprintreihe der Fakultät Mathematik 18/2012, Working Paper.

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Date of publication of this fulltext: 13 Mar 2013 09:53

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.


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Item type:Monograph (Working Paper)
Series of the University of Regensburg:Preprintreihe der Fakultät Mathematik
Date:2012
Institutions:Mathematics > Prof. Dr. Felix Finster
Keywords:Two-phase flow, Navier-Stokes equations, diffuse interface model, mixtures of viscous fluids, Cahn-Hilliard equation, degenerate mobility
Dewey Decimal Classification:500 Science > 510 Mathematics
Status:Unknown
Refereed:No, this version has not been refereed yet (as with preprints)
Created at the University of Regensburg:Yes
Item ID:27903
Owner only: item control page

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