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 ArcTanh

 http://functions.wolfram.com/01.27.27.0441.01

 Input Form

 ArcTanh[z] == (3 Pi I)/2 - I ArcCos[z/Sqrt[z^2 - 1]] /; Element[z, Reals] && z < -1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["3", "\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", FractionBox["z", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]], ")"]]]]]]

 MathML Form

 tanh - 1 ( z ) 3 π 2 - cos - 1 ( z z 2 - 1 ) /; ( z z < - 1 ) Condition z 3 2 -1 -1 z z 2 -1 1 2 -1 z z -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", FractionBox["z", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "-", "1"]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", RowBox[List["-", "1"]]]]]]]]]]]]

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

 2003-08-21