Quantum resurgence for a class of Airy type differential equations

Abstract

In this article, we investigate the resurgent properties of divergent WKB solutions of a class of Airy type perturbed differential equations. In particular, we extend and propose a new proof of a reduction theorem, due to Aoki et al. [T. Aoki, T. Kawai, Y. Takei, The Bender-Wu analysis and the Voros theory, in: Special Functions, ICM-90 Satell. Conf. Proc., Okayama, 1990, Springer, Tokyo, 1991, near a simple turning point, in the framework of exact WKB analysis. Our scheme of proof is based on a Laplace-integral representation derived from an existence theorem of holomorphic solutions for a singular linear partial differential equation.