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 ArcTanh

 http://functions.wolfram.com/01.27.27.3133.01

 Input Form

 ArcTanh[z] == (z/2) Sqrt[1/z^2] ArcSech[(z^2 - 1)/(z^2 + 1)] - (Pi Sqrt[-z^2])/(2 z)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["z", "2"], SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], RowBox[List["ArcSech", "[", FractionBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", "z"]]]]]]]]]

 MathML Form

 tanh - 1 ( z ) 1 2 z 1 z 2 sech - 1 ( z 2 - 1 z 2 + 1 ) - π - z 2 2 z z 1 2 z 1 z 2 -1 1 2 z 2 -1 z 2 1 -1 -1 -1 z 2 1 2 2 z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "z", " ", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], " ", RowBox[List["ArcSech", "[", FractionBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]]]], RowBox[List["2", " ", "z"]]]]]]]]]

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

 2003-08-21