ArcCoth[z] == 1/z + 1/(z^3 (3 + ContinueFraction[{-((1 - (-1)^k + k)^2/z^2), 3 + 2 k}, {k, 1, Infinity}])) /; !IntervalMemberQ[Interval[{-1, 1}], z]

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2001-10-29