  The generalized hypergeometric function $_qF_p$ is a power series in which
the ratio of successive terms is a rational function of the summation index.
The Gaussian hypergeometric functions $_2F_1$ and $_3F_2$ are most common
special cases of the generalized hypergeometric function $_qF_p$. The Appell
hypergeometric functions $F_q$, $q=1,2,3,4$ are product of two hypergeometric
functions $_2F_1$ that appear in many areas of mathematical physics. Here, we
are interested in the Appell hypergeometric function $F_2$ which is known to
have a double integral representation. As demonstrated by Opps, Saad, and
Srivastava (J. Math. Anal. Appl. 302 (2005) 180-195), the double integral
representation of $F_2$ can be reduced to a single integral that can be easily
evaluated for certain values of the parameters in terms of $_2F_1$ and $_3F_2$.
Using many of the reduction formulas of $_2F_1$ and $_3F_2$ and the
representation of $F_2$ in terms of a single integral, we have begun to
tabulate new reduction formulas for $F_2$.
