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 ArcTanh

 http://functions.wolfram.com/01.27.27.2264.01

 Input Form

 ArcTanh[z] == Pi I - (1/2) ArcCosh[(1 + z^2)/(1 - z^2)] /; Element[z, Reals] && z < -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "]"]]]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]], ")"]]]]]]

 MathML Form

 tanh - 1 ( z ) π - 1 2 cosh - 1 ( 1 + z 2 1 - z 2 ) /; ( z z < - 1 ) Condition z -1 1 2 1 z 2 1 -1 z 2 -1 z z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "-", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["ArcCosh", "[", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]], RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]]]]]

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

 2003-08-21