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.

Read more about this topic:  Multiplication Theorem

Famous quotes containing the word function:

    “The intension of a proposition comprises whatever the proposition entails: and it includes nothing else.... The connotation or intension of a function comprises all that attribution of this predicate to anything entails as also predicable to that thing.”
    —Clarence Lewis (1883–1964)