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 ArcSech

 http://functions.wolfram.com/01.30.27.0324.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21