# Functional equation

1. Apr 12, 2009

### 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 ??

2. Apr 12, 2009