## An integral form for a generalized zeta function.(English)Zbl 1018.11044

Summary: We extend Theorem 4 of the preceding paper [ibid. 22, 91-97 (2002; Zbl 1018.11043)] as follows: $\zeta(z;a)= \sum_{i=0}^{k-1} \frac{1}{\Gamma(z)} \int_0^\infty \frac {t^{z-1} e^{-(a+i)t}} {1-e^{-kt}} dt \qquad (\operatorname{Re} z> 1),$ where $$\zeta(z;a)= \sum_{m=0}^\infty \frac{1} {(a+m)^z}$$ $$(\operatorname{Re} z>1)$$, and $$a>0$$ and $$k>1$$ is a fixed positive integer.

### MSC:

 11M35 Hurwitz and Lerch zeta functions 26A33 Fractional derivatives and integrals

Zbl 1018.11043