Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic   Cylinder Functions
  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. 
Felix Finster and Joel Smoller
math.CA math-ph math.MP