Given the function $Z(s,N)= \sum \limits_{n=1}^{N}n^{-s}$.
In the limit $N \to \infty$ the function $Z(s,N) \to \zeta (s)$ Riemann Zeta function.
My question is: Is there a Functional equation for this function? I mean a relationship of the form $ Z(s,N)=G(s) Z(1-s,N)$.