  We suggest an approximation for the zero-balanced Appell hypergeometric
function $F_1$ near the singular point $(1,1)$. Our approximation can be viewed
as a generalization of Ramanujan's approximation for zero-balanced ${_2F_1}$
and is expressed in terms of ${_3F_2}$. We find an error bound and prove some
basic properties of the suggested approximation which reproduce the similar
properties of the Appell function. Our approximation reduces to the
approximation of Carlson-Gustafson when the Appell function reduces to the
first incomplete elliptic integral.
