Zeta[-n, a] \[Proportional] (-(1/(n + 1))) Sum[Binomial[n + 1, k] BernoulliB[n - k + 1] a^k, {k, 0, n + 1}] + Sum[((k + a)^2)^(n/2) - (k + a)^n, {k, 0, Floor[-Re[a]]}] /; Element[n, Integers] && n >= 0

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2007-05-02