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In a previous work ([Eb]), the author proposed a method employing contiguityrelations to derive hypergeometric series in closed form. In [Eb], this methodwas used to derive Gauss's hypergeometric series $_2F_1$ possessing closedforms. Here, we consider the application of this method to Appell'shypergeometetric series $F_1$ and derive several $F_1$ possessing closed forms.Moreover, analyzing these $F_1$, we obtain values of $_2F_1$ with no freeparameters. 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.

Special values of Gauss's hypergeometric series derived from Appell's series $F_1$ with closed forms