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 ArcSech

 http://functions.wolfram.com/01.30.27.2098.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21