An elementary proof of the Voros connection formula for WKB solutions to the Airy equation with a large parameter

TL;DR

This paper provides a straightforward proof of the Voros connection formula for WKB solutions to the Airy equation with a large parameter, and extends some results to the Pearcey system, a two-variable generalization.

Contribution

It offers an elementary proof of the Voros connection formula and generalizes parts of the results to the Pearcey system.

Findings

Proof of the Voros connection formula using cubic equations

Extension of results to the Pearcey system

Simplification of existing proofs for WKB solutions

Abstract

The Voros connection formula for WKB solutions to the Airy equation with a large parameter is proved by using cubic equations. Some parts of the results are generalized to the Pearcey system, which is a two-variable version of the Airy equation, is given.