generalized zeta function
The generalized zeta function is defined for $\sigma \u2a7e1+\delta $ by
$$\zeta (s,a)=\sum _{n=0}^{\mathrm{\infty}}\frac{1}{{(a+n)}^{s}},$$ |
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 |
---|---|
Canonical name | GeneralizedZetaFunction |
Date of creation | 2013-03-22 16:11:35 |
Last modified on | 2013-03-22 16:11:35 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 7 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 11M35 |