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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)$.

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    $\text{}{}n=0$?2011-12-02
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    "... in the limit $N \to \infty$ ...": this claim is only true if $\Re(s) > 1$.2011-12-03
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    OH. sorry :( i meant n=1 :) otherwise the series would be divergent ...2011-12-03
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    Edited in accord with comments above.2012-02-27

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