Voros Coefficients at the Origin and at the Infinity of the Generalized Hypergeometric Differential Equations with a Large Parameter

TL;DR

This paper derives explicit forms of Voros coefficients for generalized hypergeometric differential equations with large parameters at both origin and infinity, demonstrating their Borel summability in certain parameter regions.

Contribution

It provides the first explicit formulas for Voros coefficients at both singular points and analyzes their Borel summability properties.

Findings

Explicit formulas for Voros coefficients at origin and infinity

Borel summability of these coefficients in specific parameter regions

Borel sums are explicitly computed in these regions

Abstract

Voros coefficients of the generalized hypergeometric differential equations with a large parameter are defined and their explicit forms are given for the origin and for the infinity. It is shown that they are Borel summable in some specified regions in the space of parameters and their Borel sums in the regions are given.