  In this article we propose an extension of Appell hypergeometric function
$F_2$ (or equivalently $F_3$). It is derived from a particular solution of a
higher order Painlev\'e system in two variables. On the other hand, an
extension of Appell's $F_1$ was introduced by Tsuda. We also show that those
two extensions are equivalent at the level of systems of linear partial
differential equations.
