  In my joint papers with Iwaki and Koike ([IKoT1, IKoT2]) we found an
intriguing relation between the Voros coefficients in the exact WKB analysis
and the free energy in the topological recursion introduced by Eynard and
Orantin in the case of the confluent family of the Gauss hypergeometric
differential equations. In this paper we discuss its generalization to the case
of the hypergeometric differential equations associated with $2$-dimensional
degenerate Garnier systems.
