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 ArcTanh

 http://functions.wolfram.com/01.27.27.0851.01

 Input Form

 ArcTanh[(2 z)/(1 + z^2)] == -2 I ArcTan[I/z] /; Abs[z] > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[RowBox[List["2", " ", "z"]], RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox["\[ImaginaryI]", "z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]

 MathML Form

 tanh - 1 ( 2 z z 2 + 1 ) - 2 tan - 1 ( z ) /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 Condition 2 z z 2 1 -1 -2 z -1 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List["2", " ", "z_"]], RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", RowBox[List["ArcTan", "[", FractionBox["\[ImaginaryI]", "z"], "]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2003-08-21