### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 002, 23 pages      arXiv:2104.13751      https://doi.org/10.3842/SIGMA.2022.002

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

Takashi Aoki a and Shofu Uchida b
a) Department of Mathematics, Kindai University, Higashi-Osaka 577-8502, Japan
b) Graduate School of Science and Engineering, Kindai University, Higashi-Osaka 577-8502, Japan

Received July 20, 2021, in final form December 30, 2021; Published online January 03, 2022

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.

Key words: exact WKB analysis; Voros coefficients; generalized hypergeometric differential equations.

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