Kummer's Theorem

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

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

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