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 ArcTanh

 http://functions.wolfram.com/01.27.27.2130.01

 Input Form

 ArcTanh[Sqrt[-1 - z]/Sqrt[-z]] == (Pi I)/2 + ArcSinh[Sqrt[z]] /; Im[z] < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]], SqrtBox[RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z_"]]], SqrtBox[RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], "+", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "<", "0"]]]]]]]]

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

 2003-08-21