HarmonicNumber[z] == HarmonicNumber[Subscript[z, 0]] + Sum[(-1)^k (HarmonicNumber[Subscript[z, 0], k + 1] - Zeta[k + 1]) (z - Subscript[z, 0])^k, {k, 1, Infinity}] /; !(Element[Subscript[z, 0], Integers] && Subscript[z, 0] < 0)

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2007-05-02