Definition:Hurwitz Zeta Function

Definition

The Hurwitz zeta function is defined for $\set {\map \Re s > 1, a \ne 0, -1, -2, \cdots}$ as the series:

$\ds \map \zeta {s, a} = \sum_{n \mathop = 0}^\infty \frac 1 {\paren {n + a}^s}$

Also see

• Definition:Riemann Zeta Function of which the Hurwitz zeta function is a generalization

• Definition:Lerch Transcendent, of which $\map \zeta {s, a}$ is a special case

• Results about the Hurwitz zeta function can be found here.

Source of Name

This entry was named for Adolf Hurwitz.

Sources

• 1920: E.T. Whittaker and G.N. Watson: A Course of Modern Analysis (3rd ed.): $13.11$: The generalised Zeta-function