1207.6861 (Felix Finster et al.)

Absence of Zeros and WKB Error Estimates for Airy and Parabolic Cylinder
Functions    [PDF]

Felix Finster, Joel Smoller

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 analyze a limiting case where the parabolic cylinder functions go over to the Airy function.

View original: http://arxiv.org/abs/1207.6861