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 ArcTanh

 http://functions.wolfram.com/01.27.27.2494.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21