Euler product for the gamma function
= Euler product for the gamma function
{c}
For $z$ away from the poles, the <gamma function> satisfies
$$
\Gamma(z)=\frac1z\prod_{n=1}^\infty(1+1/n)^z(1+z/n)^{-1}.
$$
Its finite product is $m!(m+1)^z/[z(z+1)\cdots(z+m)]$. Splitting even and odd factors gives the <gamma duplication formula>.