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/01.30.27.0129.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

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

 2003-08-21