# generalized zeta function

The generalized zeta function is defined for $\sigma\geqslant 1+\delta$ by

 $\zeta(s,a)=\sum_{n=0}^{\infty}\frac{1}{(a+n)^{s}},$

where $a$ is a constant. Clearly, $\zeta(s,1)=\zeta(s)$, where $\zeta(s)$ is the Riemann zeta function.

## References

• 1 Hurwitz, Zeitschritf für Math. und Phys. xxvii. (1882), pp. 86-101.
Title generalized zeta function GeneralizedZetaFunction 2013-03-22 16:11:35 2013-03-22 16:11:35 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Definition msc 11M35