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 ArcTanh

 http://functions.wolfram.com/01.27.27.2189.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21