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 ArcTanh

 http://functions.wolfram.com/01.27.27.0768.01

 Input Form

 ArcTanh[z/(Sqrt[1 + z^2] + 1)] == (I/2) ArcCos[I z] - (Pi I)/4

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcTanh", "[", FractionBox["z", RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]]], "+", "1"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["ArcCos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]]]]]]

 MathML Form

 tanh - 1 ( z z 2 + 1 + 1 ) 2 cos - 1 ( z ) - π 4 z z 2 1 1 2 1 -1 2 -1 z -1 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTanh", "[", FractionBox["z_", RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["z_", "2"]]]], "+", "1"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["ArcCos", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "4"]]]]]]]

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

 2003-08-21