ArcCoth[Coth[z]] == Piecewise[{{z - Pi I Floor[(2 Im[z] - Pi)/(2 Pi)], Element[(2 Im[z] + Pi)/(2 Pi), Integers] && Re[z] <= 0}, {z - Pi I Floor[(2 Im[z] + Pi)/(2 Pi)], True}}]

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2007-05-02