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; }

 ArcCsc

 http://functions.wolfram.com/01.17.16.0147.01

 Input Form

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

 Standard Form

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

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

 Rule Form

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

 2007-05-02