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 ArcTanh

 http://functions.wolfram.com/01.27.27.3129.01

 Input Form

 ArcTanh[z] == (Pi I)/2 + (1/2) ArcSech[(z^2 - 1)/(z^2 + 1)] /; 0 < Arg[z] < Pi/2

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSech", "[", FractionBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]]]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 tanh - 1 ( z ) π 2 + 1 2 sech - 1 ( z 2 - 1 z 2 + 1 ) /; 0 < arg ( z ) < π 2 Condition z 2 -1 1 2 z 2 -1 z 2 1 -1 0 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSech", "[", FractionBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2003-08-21