  We study a connection problem between the fundamental systems of solutions at
singular points $0$ and $1$ for the generalized hypergeometric equation which
is satisfied by the generalized hypergeometric series ${}_nF_{n-1}$. In
general, the local solution space around $x=1$ consists of one dimensional
singular solution space and $n-1$ dimensional holomorphic solution space.
Therefore in the case of $n\ge3$, the expression of connection matrix depends
on the choice of the fundamental system of solutions at $x=1$. On the
connection problem for ordinary differential equations, Sch\"{a}fke and Schmidt
(LNM 810, Springer, 1980) gave an impressive idea which focuses on the series
expansion of fundamental system of solutions. We apply their idea to solve the
connection problem for the generalized hypergeometric equation and derive the
connection matrix.

Classical Analysis and ODEs