  In a previous work ([Eb]), the author proposed a method employing contiguity
relations to derive hypergeometric series in closed form. In [Eb], this method
was used to derive Gauss's hypergeometric series $_2F_1$ possessing closed
forms. Here, we consider the application of this method to Appell's
hypergeometetric series $F_1$ and derive several $F_1$ possessing closed forms.
Moreover, analyzing these $F_1$, we obtain values of $_2F_1$ with no free
parameters. Some of these results provide new examples of algebraic values of
$_2F_1$.
  Key Words and Phrases: Gauss's hypergeometric series, algebraic value,
Appell's hypergeometric series, hypergeometric identity.
