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/01.30.16.0184.01

 Input Form

 ArcSech[x] + Log[y] == I Pi (1 - (-1)^(Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y + 1]/ (2 Pi))] - Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y]/ (2 Pi))])) + (-1)^(Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y]/Pi)] - Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y - 1]/(2 Pi))] + Floor[Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y]/Pi - (2 Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y - 1])/Pi] + Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y + 1]/(2 Pi))]) ArcSech[(2 (Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x) y)/ ((Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^2 y^2 + 1)] - 2 I Pi Floor[(-Arg[Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x] - Arg[y] + Pi)/(2 Pi)]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["ArcSech", "[", "x", "]"]], "+", RowBox[List["Log", "[", "y", "]"]]]], "\[Equal]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]], "-", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "]"]], "\[Pi]"]]], "]"]], "-", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "-", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]], "+", RowBox[List["Floor", "[", RowBox[List[FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "]"]], "\[Pi]"], "-", FractionBox[RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "-", "1"]], "]"]]]], "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]], " ", RowBox[List["ArcSech", "[", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], "2"], " ", SuperscriptBox["y", "2"]]], "+", "1"]]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], "]"]]]], "-", RowBox[List["Arg", "[", "y", "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]]]

 MathML Form

 sech - 1 ( x ) + log ( y ) π ( 1 - ( - 1 ) - arg ( ( 1 x - 1 1 + 1 x + 1 x ) y + 1 ) 2 π - - arg ( ( 1 x - 1 1 + 1 x + 1 x ) y ) 2 π ) + ( - 1 ) arg ( ( 1 x - 1 1 + 1 x + 1 x ) y ) π - 2 arg ( ( 1 x - 1 1 + 1 x + 1 x ) y - 1 ) π + - arg ( ( 1 x - 1 1 + 1 x + 1 x ) y ) π - - arg ( ( 1 x - 1 1 + 1 x + 1 x ) y - 1 ) 2 π + - arg ( ( 1 x - 1 1 + 1 x + 1 x ) y + 1 ) 2 π sech - 1 ( 2 ( 1 x - 1 1 + 1 x + 1 x ) y ( 1 x - 1 1 + 1 x + 1 x ) 2 y 2 + 1 ) - 2 π - arg ( 1 x - 1 1 + 1 x + 1 x ) - arg ( y ) + π 2 π x y 1 -1 -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y 1 2 -1 -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y 2 -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y -1 -1 2 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y -1 -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y -1 -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y -1 2 -1 -1 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y 1 2 -1 2 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 y 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 2 y 2 1 -1 -1 2 -1 1 x -1 -1 1 2 1 1 x -1 1 2 1 x -1 -1 y 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcSech", "[", "x_", "]"]], "+", RowBox[List["Log", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]], "-", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "]"]], "\[Pi]"]]], "]"]], "-", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "-", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]], "+", RowBox[List["Floor", "[", RowBox[List[FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "]"]], "\[Pi]"], "-", FractionBox[RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "-", "1"]], "]"]]]], "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List["Arg", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], "+", "1"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]]]], "]"]]]]], " ", RowBox[List["ArcSech", "[", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], " ", "y"]], RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], ")"]], "2"], " ", SuperscriptBox["y", "2"]]], "+", "1"]]], "]"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List[RowBox[List[SqrtBox[RowBox[List[FractionBox["1", "x"], "-", "1"]]], " ", SqrtBox[RowBox[List["1", "+", FractionBox["1", "x"]]]]]], "+", FractionBox["1", "x"]]], "]"]]]], "-", RowBox[List["Arg", "[", "y", "]"]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]

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

 2007-05-02