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 ArcTanh

 http://functions.wolfram.com/01.27.27.2140.01

 Input Form

 ArcTanh[Sqrt[-z]/Sqrt[-1 - z]] == ArcSinh[Sqrt[z]] /; Abs[Arg[z]] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["-", "z"]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z"]]]], "]"]], "\[Equal]", RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 tanh - 1 ( - z - 1 - z ) sinh - 1 ( z ) /; "\[LeftBracketingBar]" arg ( z ) "\[RightBracketingBar]" < π Condition -1 z 1 2 -1 -1 z 1 2 -1 z 1 2 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox[SqrtBox[RowBox[List["-", "z_"]]], SqrtBox[RowBox[List[RowBox[List["-", "1"]], "-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ArcSinh", "[", SqrtBox["z"], "]"]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-08-21