HarmonicNumber[z, r] == ((-1)^r/(r - 1)!) ((D[(1/Gamma[z + 1]) D[Gamma[z + 1], {z, 1}], {z, r - 1}] /. {z -> 0}) - D[(1/Gamma[z + 1]) D[Gamma[z + 1], {z, 1}], {z, r - 1}]) /; Element[r, Integers] && r > 0

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2007-05-02