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; }

 ArcSec

 http://functions.wolfram.com/01.18.16.0176.01

 Input Form

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

 Standard Form

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

 MathML Form

 sec - 1 ( x ) - tanh - 1 ( y ) 1 2 π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( - 1 - 1 x 2 y - 1 x 1 - y 2 ) π ) arg ( 1 - 1 x 2 - x ) + arg ( + y 1 - y 2 ) 2 π + ( - 1 ) 1 2 - arg ( - 1 - 1 x 2 y - 1 x 1 - y 2 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( - 1 - 1 x 2 y - 1 x 1 - y 2 ) π ) 1 2 - arg ( 1 - 1 x 2 - x ) + arg ( + y 1 - y 2 ) 2 π + 2 ) - sec - 1 ( ( - 1 ) - 1 2 - arg ( - 1 - 1 x 2 y - 1 x 1 - y 2 ) π 1 - y 2 y x - 1 - 1 x 2 ) x -1 y 1 2 2 1 -1 1 2 -1 -1 1 -1 1 x 2 -1 1 2 y -1 1 x -1 1 -1 y 2 1 2 -1 -1 1 -1 1 x 2 -1 1 2 -1 x -1 y 1 -1 y 2 1 2 -1 2 -1 -1 1 2 -1 -1 1 -1 1 x 2 -1 1 2 y -1 1 x -1 1 -1 y 2 1 2 -1 -1 -1 2 -1 -1 1 2 -1 -1 1 -1 1 x 2 -1 1 2 y -1 1 x -1 1 -1 y 2 1 2 -1 -1 1 2 -1 1 -1 1 x 2 -1 1 2 -1 x -1 y 1 -1 y 2 1 2 -1 2 -1 2 -1 -1 -1 1 2 -1 -1 1 -1 1 x 2 -1 1 2 y -1 1 x -1 1 -1 y 2 1 2 -1 -1 1 -1 y 2 1 2 y x -1 -1 1 -1 1 x 2 -1 1 2 -1 [/itex]

 Rule Form

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

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

 2007-05-02