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 ArcTanh

 http://functions.wolfram.com/01.27.27.3402.01

 Input Form

 ArcTanh[z/Sqrt[z^2 - 1]] == ArcSech[1/z] + (Pi I)/2 /; -(Pi/2) < Arg[z] < 0

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21