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 ArcTanh

 http://functions.wolfram.com/01.27.27.2053.01

 Input Form

 ArcTanh[1/Sqrt[z]] == (1/2) ArcSinh[(2 Sqrt[z])/(z - 1)] /; Abs[z] > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[StyleBox["1", "Program"], SqrtBox["z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], RowBox[List["ArcSinh", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["z", "-", "1"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]

 MathML Form

 tanh - 1 ( 1 z ) 1 2 sinh - 1 ( 2 z z - 1 ) /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 Condition 1 z 1 2 -1 1 2 2 z 1 2 z -1 -1 z 1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox["1", SqrtBox["z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcSinh", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["z", "-", "1"]]], "]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]]]]]]]]

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

 2003-08-21