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.

Read more about this topic:  Hurwitz Zeta Function

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