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 ArcSech

 http://functions.wolfram.com/01.30.27.1560.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21