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

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Finster, Felix ; Smoller, Joel
Date of publication of this fulltext: 13 Mar 2013 09:53


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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