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 ArcTanh

 http://functions.wolfram.com/01.27.27.2669.01

 Input Form

 ArcTanh[(2 z)/(1 + z^2)] == 2 ArcCoth[1/z] + (Sqrt[-z^2]/z) Pi /; 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", " ", RowBox[List["ArcCoth", "[", FractionBox["1", "z"], "]"]]]], "+", RowBox[List[FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], "z"], "\[Pi]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]

 MathML Form

 tanh - 1 ( 2 z 1 + z 2 ) 2 coth - 1 ( 1 z ) + π - z 2 z /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 Condition 2 z 1 z 2 -1 2 1 z -1 -1 z 2 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", " ", RowBox[List["ArcCoth", "[", FractionBox["1", "z"], "]"]]]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], " ", "\[Pi]"]], "z"]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]]]

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

 2003-08-21