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 ArcSech

 http://functions.wolfram.com/01.30.27.2344.01

 Input Form

 ArcSech[(1 - z^2)/(1 + z^2)] == Pi I - 2 ArcCoth[z] /; Inequality[-Pi, Less, Arg[z], LessEqual, -(Pi/2)]

 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["\[Pi]", " ", "\[ImaginaryI]"]], "-", RowBox[List["2", RowBox[List["ArcCoth", "[", "z", "]"]]]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 sech - 1 ( 1 - z 2 1 + z 2 ) π - 2 coth - 1 ( z ) /; - π < arg ( z ) - π 2 Condition 1 -1 z 2 1 z 2 -1 -1 2 z Inequality -1 z -1 2 -1 [/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["\[Pi]", " ", "\[ImaginaryI]"]], "-", RowBox[List["2", " ", RowBox[List["ArcCoth", "[", "z", "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", RowBox[List["-", FractionBox["\[Pi]", "2"]]]]]]]]]]]

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

 2003-08-21