Multiplication Theorem - Hurwitz Zeta Function

Hurwitz Zeta Function

For the Hurwitz zeta function generalizes the polygamma function to non-integer orders, and thus obeys a very similar multiplication theorem:

where is the Riemann zeta function. This is a special case of

and

Multiplication formulas for the non-principal characters may be given in the form of Dirichlet L-functions.