generalized zeta function

The generalized zeta function is defined for $\sigma ⩾1+\delta$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.