  In this paper, we present a new method for finding identities for
hypergeoemtric series, such as the (Gauss) hypergeometric series, the
generalized hypergeometric series and the Appell-Lauricella hypergeometric
series. Furthermore, using this method, we get identities for the
hypergeometric series $F(a,b;c;x)$; we show that values of $F(a,b;c;x)$ at some
points $x$ can be expressed in terms of gamma functions, together with certain
elementary functions. We tabulate the values of $F(a,b;c;x)$ that can be
obtained with this method. We find that this set includes almost all previously
known values and many previously unknown values.
  Key Words and Phrases: hypergeometric series, three term relation, special
value, solving polynomial systems.
