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arXiv · 1207.6861

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

Felix Finster·Joel Smoller
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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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Felix Finster, Joel Smoller. 2013-04-15. Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic Cylinder Functions. https://doi.org/10.4310/cms.2014.v12.n1.a8

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