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 ArcTanh

 http://functions.wolfram.com/01.27.27.2472.01

 Input Form

 ArcTanh[Sqrt[1 - z]] == ((Pi I)/2) (Sqrt[z] Sqrt[1/z] - 1) + ArcCosh[Sqrt[1/z]]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List["ArcTanh", "[", SqrtBox[RowBox[List["1", "-", "z"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "2"], RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], SqrtBox[FractionBox["1", "z"]]]], "-", "1"]], ")"]]]], "+", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]]]]]]

 MathML Form

 tanh - 1 ( 1 - z ) π 2 ( z 1 z - 1 ) + cosh - 1 ( 1 z ) 1 -1 z 1 2 2 -1 z 1 2 1 z -1 1 2 -1 1 z -1 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", SqrtBox[RowBox[List["1", "-", "z_"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["z"], " ", SqrtBox[FractionBox["1", "z"]]]], "-", "1"]], ")"]]]], "+", RowBox[List["ArcCosh", "[", SqrtBox[FractionBox["1", "z"]], "]"]]]]]]]]

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

 2003-08-21