Hurwitz Zeta Function - Functional Equation

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]

holds for all values of s.

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