Parametric Stokes phenomena of the Gauss hypergeometric differential equation with a large parameter

Abstract

Stokes phenomena with respect to parameters are investigated for the Gauss hypergeometric differential equation with a large parameter. For this purpose, the notion of the Voros coefficient is introduced for the equation. The explicit forms of the Voros coefficients are given as well as their Borel sums. By using them, formulas which describe the Stokes phenomena are obtained.