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 ArcTanh

 http://functions.wolfram.com/01.27.27.2373.01

 Input Form

 ArcTanh[Sqrt[z]] == (Pi I)/2 - ArcCosh[Sqrt[z/(z - 1)]] /; Element[z, Reals] && z < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], "]"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "\[And]", RowBox[List["z", "<", "0"]]]], ")"]]]]]]

 MathML Form

 tanh - 1 ( z ) - cosh - 1 ( z z - 1 ) + π 2 /; ( z z < 0 ) Condition z 1 2 -1 z z -1 -1 1 2 2 -1 z z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", SqrtBox["z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "-", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["z", RowBox[List["z", "-", "1"]]]], "]"]]]], "/;", RowBox[List[RowBox[List["z", "\[Element]", "Reals"]], "&&", RowBox[List["z", "<", "0"]]]]]]]]]]

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

 2003-08-21