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 ArcTanh

 http://functions.wolfram.com/01.27.27.1917.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21