Functional Equation for $\sum_{n=0}^{N}n^{k}$

[zetafunction]

is there a functional equation for

$$\sum_{n=0}^{N}n^{k}=Z(N,k)$$

where k and N are real numbers, in case N tends to infinite we could consider the functional equation of Riemann zeta but what happens in the case of N finite ??

 

[qntty]

Here's the relevant Mathworld article.