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 ArcSech

 http://functions.wolfram.com/01.30.27.1775.01

 Input Form

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

 Standard Form

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

 MathML Form

 sech - 1 ( z ) - π + cosh - 1 ( 1 z 2 ) /; π 2 arg ( z ) < π Condition z -1 1 z 2 -1 1 2 Inequality 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["ArcCosh", "[", SqrtBox[FractionBox["1", SuperscriptBox["z", "2"]]], "]"]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]]]

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

 2003-08-21