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/01.18.16.0178.01

 Input Form

 ArcSec[x] - ArcCoth[y] == -2 I Pi (Floor[(-Arg[(Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y]] + (1/2) Arg[1 + 1/y] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[(Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y]]])/(2 Pi)] + Floor[((1/2) Im[Log[1 + 1/y]] + Pi)/(2 Pi)]) - 2 I Pi (Floor[(-Arg[(Sqrt[1 - 1/x^2] + I/x)^I] - (1/2) Arg[1 - 1/y] + Pi)/ (2 Pi)] + Floor[(Pi - (1/2) Im[Log[1 - 1/y]])/(2 Pi)] + Floor[(Pi - Re[Log[Sqrt[1 - 1/x^2] + I/x]])/(2 Pi)]) + I (1 - (-1)^(Floor[-(Arg[((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])/ Sqrt[1 + 1/y] + 1]/(2 Pi))] - Floor[-(Arg[((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])/Sqrt[1 + 1/y]]/ (2 Pi))])) Pi - I (-1)^(Floor[Arg[((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])/Sqrt[1 + 1/y] - 1]/(2 Pi) - Arg[((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])/ Sqrt[1 + 1/y] + 1]/(2 Pi) + 1/2] + Floor[-(Arg[((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])/Sqrt[1 + 1/y]]/ Pi)]) ArcSec[(2 (Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])/ ((((Sqrt[1 - 1/x^2] + I/x)^(2 I) (1 - 1/y))/(1 + 1/y) + 1) Sqrt[1 + 1/y])] + Pi/2

 Standard Form

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

 MathML Form

 sec - 1 ( x ) - coth - 1 ( y ) - 2 π ( 1 2 arg ( 1 + 1 y ) - arg ( ( 1 - 1 x 2 + x ) 1 - 1 y ) + π 2 π + 1 2 Im ( log ( 1 + 1 y ) ) + π 2 π + π - Im ( log ( ( 1 - 1 x 2 + x ) 1 - 1 y ) ) 2 π ) - 2 π ( - arg ( ( 1 - 1 x 2 + x ) ) - 1 2 arg ( 1 - 1 y ) + π 2 π + π - 1 2 Im ( log ( 1 - 1 y ) ) 2 π + π - Re ( log ( 1 - 1 x 2 + x ) ) 2 π ) + ( 1 - ( - 1 ) - arg ( 1 - 1 y ( 1 - 1 x 2 + x ) 1 + 1 y + 1 ) 2 π - - arg ( ( 1 - 1 x 2 + x ) 1 - 1 y 1 + 1 y ) 2 π ) π - ( - 1 ) arg ( ( 1 - 1 x 2 + x ) 1 - 1 y 1 + 1 y - 1 ) 2 π + 1 2 - arg ( 1 - 1 y ( 1 - 1 x 2 + x ) 1 + 1 y + 1 ) 2 π + - arg ( ( 1 - 1 x 2 + x ) 1 - 1 y 1 + 1 y ) π sec - 1 ( 2 ( 1 - 1 x 2 + x ) 1 - 1 y ( ( 1 - 1 y ) ( 1 - 1 x 2 + x ) 2 1 + 1 y + 1 ) 1 + 1 y ) + π 2 x -1 y -2 1 2 1 1 y -1 -1 1 -1 1 x 2 -1 1 2 x -1 1 -1 1 y -1 1 2 2 -1 1 2 1 1 y -1 2 -1 -1 1 -1 1 x 2 -1 1 2 x -1 1 -1 1 y -1 1 2 2 -1 -1 2 -1 1 -1 1 x 2 -1 1 2 x -1 -1 1 2 1 -1 1 y -1 2 -1 -1 1 2 1 -1 1 y -1 2 -1 -1 1 -1 1 x 2 -1 1 2 x -1 2 -1 1 -1 -1 -1 1 -1 1 y -1 1 2 1 -1 1 x 2 -1 1 2 x -1 1 1 y -1 1 2 -1 1 2 -1 -1 -1 1 -1 1 x 2 -1 1 2 x -1 1 -1 1 y -1 1 2 1 1 y -1 1 2 -1 2 -1 -1 -1 1 -1 1 x 2 -1 1 2 x -1 1 -1 1 y -1 1 2 1 1 y -1 1 2 -1 -1 2 -1 1 2 -1 1 -1 1 y -1 1 2 1 -1 1 x 2 -1 1 2 x -1 1 1 y -1 1 2 -1 1 2 -1 -1 1 -1 1 x 2 -1 1 2 x -1 1 -1 1 y -1 1 2 1 1 y -1 1 2 -1 -1 2 1 -1 1 x 2 -1 1 2 x -1 1 -1 1 y -1 1 2 1 -1 1 y -1 1 -1 1 x 2 -1 1 2 x -1 2 1 1 y -1 -1 1 1 1 y -1 1 2 -1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcSec", "[", "x_", "]"]], "-", RowBox[List["ArcCoth", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["Arg", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], "\[ImaginaryI]"], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", "y"]]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Arg", "[", RowBox[List["1", "+", FractionBox["1", "y"]]], "]"]]]], "+", "\[Pi]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], "+", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["Log", "[", 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RowBox[List["-", FractionBox[RowBox[List["Arg", "[", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], "\[ImaginaryI]"], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", "y"]]]]]], SqrtBox[RowBox[List["1", "+", FractionBox["1", "y"]]]]], "]"]], "\[Pi]"]]], "]"]]]]], " ", RowBox[List["ArcSec", "[", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], "\[ImaginaryI]"], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", "y"]]]]]], RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["x", "2"]]]]], "+", FractionBox["\[ImaginaryI]", "x"]]], ")"]], RowBox[List["2", " ", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02