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## Main Question or Discussion Point

is there a functional equation for

[tex] \sum_{n=0}^{N}n^{k}=Z(N,k) [/tex]

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 ??

[tex] \sum_{n=0}^{N}n^{k}=Z(N,k) [/tex]

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 ??