  We consider the generalized eigenvalue problem for the classical Euler
differential equation and demonstrate its intimate connection with Meijer's
$G$-functions. In the course of deriving the solution of the generalized Euler
eigenvalue equation we review some of the basics of generalized hypergeometric
functions and Meijer's $G$-functions and some of its special cases where the
underlying Mellin-type integrand exhibits higher-order poles.
