html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 ArcSech

 http://functions.wolfram.com/01.30.27.1570.01

 Input Form

 ArcSech[z] == (-Pi) I - ArcSinh[Sqrt[1 - z^2]/z] /; 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["ArcSinh", "[", FractionBox[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], "z"], "]"]]]]]], "/;", RowBox[List[FractionBox["\[Pi]", "2"], "\[LessEqual]", RowBox[List["Arg", "[", "z", "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

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

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

 2003-08-21