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/01.30.27.1533.01

 Input Form

 ArcSech[z] == (Sqrt[1/z - 1]/Sqrt[1 - 1/z]) (Pi/2 + I ArcSinh[I/z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["ArcSech", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List[RowBox[List["1", "/", "z"]], "-", "1"]]], " "]], SqrtBox[RowBox[List["1", "-", RowBox[List["1", "/", "z"]]]]]], RowBox[List["(", RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", FractionBox["\[ImaginaryI]", "z"], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 sech - 1 ( z ) 1 1 - 1 z 1 z - 1 ( sinh - 1 ( z ) + π 2 ) z 1 1 -1 1 z -1 1 2 -1 1 z -1 -1 1 2 z -1 2 -1 [/itex]

 Rule Form

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

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

 2003-08-21