Functional Equation
The functional equation relates values of the zeta on the left- and right-hand sides of the complex plane. For integers ,
![\zeta \left(1-s,\frac{m}{n} \right) =
\frac{2\Gamma(s)}{ (2\pi n)^s }
\sum_{k=1}^n \left[\cos
\left( \frac {\pi s} {2} -\frac {2\pi k m} {n} \right)\;
\zeta \left( s,\frac {k}{n} \right)\right]](http://upload.wikimedia.org/math/c/7/6/c76111a861d49dae418bc7da47734a6e.png)
holds for all values of s.
Read more about this topic: Hurwitz Zeta Function
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