ABSENCE OF ZEROS AND ASYMPTOTIC ERROR ESTIMATES FOR AIRY AND PARABOLIC CYLINDER FUNCTIONS

作者：Finster Felix^*; Smoller Joel

来源：Communications in Mathematical Sciences, 2014, 12(1): 175-200.

• Airy functions
• parabolic cylinder functions
• asymptotic error estimates

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.

• 出版日期2014