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Kummer's Theorem


\begin{displaymath}
{}_2F_1(x, -x;x+n+1; -1) = {\Gamma(x+n+1)\Gamma({\textstyle{...
...2}}n+1)\over
\Gamma(x+{\textstyle{1\over 2}}n+1)\Gamma(n+1)}
\end{displaymath}


\begin{displaymath}
{}_2F_1(\alpha, \beta; 1+\alpha-\beta; -1)
= {\Gamma(1+\alp...
...\Gamma(1+\alpha)\Gamma(1+{\textstyle{1\over 2}}\alpha-\beta)},
\end{displaymath}

where ${}_2F_1(a,b;c;z)$ is a Hypergeometric Function and $\Gamma(z)$ is the Gamma Function.




© 1996-9 Eric W. Weisstein
1999-05-26