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/01.17.16.0175.01

 Input Form

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

 Standard Form

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

 MathML Form

 csc - 1 ( x ) - cosh - 1 ( y ) - csc - 1 ( ( - 1 ) - 1 2 - arg ( - y x + 1 - 1 x 2 y - 1 y + 1 ) π - 1 - 1 x 2 y - y - 1 y + 1 x ) - 1 2 π ( 1 2 ( 1 - ( - 1 ) - - arg ( 1 - y ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 - 1 x 2 1 - y 2 - y x ) π ) arg ( 1 - 1 x 2 + x ) + arg ( y + 1 - y 2 ) 2 π + ( - 1 ) 1 2 - arg ( 1 - 1 x 2 1 - y 2 - y x ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 - 1 x 2 1 - y 2 - y x ) π ) 1 2 - arg ( 1 - 1 x 2 + x ) + arg ( y + 1 - y 2 ) 2 π ) - 1 2 ( 1 + ( - 1 ) - - arg ( 1 - y ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( y x + 1 - 1 x 2 1 - y 2 ) π ) arg ( 1 - 1 x 2 - x ) + arg ( y + 1 - y 2 ) 2 π + ( - 1 ) 1 2 - arg ( y x + 1 - 1 x 2 1 - y 2 ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( y x + 1 - 1 x 2 1 - y 2 ) π ) 1 2 - arg ( 1 - 1 x 2 - x ) + arg ( y + 1 - y 2 ) 2 π ) ) x -1 y -1 -1 -1 1 2 -1 -1 y x -1 1 -1 1 x 2 -1 1 2 y -1 1 2 y 1 1 2 -1 -1 1 -1 1 x 2 -1 1 2 y -1 y -1 1 2 y 1 1 2 x -1 -1 -1 1 2 1 2 1 -1 -1 -1 -1 1 -1 y 2 -1 2 -1 -1 1 2 -1 1 -1 1 x 2 -1 1 2 1 -1 y 2 1 2 -1 y x -1 -1 1 -1 1 x 2 -1 1 2 x -1 y 1 -1 y 2 1 2 2 -1 -1 1 2 -1 1 -1 1 x 2 -1 1 2 1 -1 y 2 1 2 -1 y x -1 -1 2 1 -1 1 2 -1 1 -1 1 x 2 -1 1 2 1 -1 y 2 1 2 -1 y x -1 -1 1 2 -1 1 -1 1 x 2 -1 1 2 x -1 y 1 -1 y 2 1 2 2 -1 -1 1 2 1 -1 -1 -1 1 -1 y 2 -1 2 -1 -1 1 2 -1 y x -1 1 -1 1 x 2 -1 1 2 1 -1 y 2 1 2 -1 1 -1 1 x 2 -1 1 2 -1 x -1 y 1 -1 y 2 1 2 2 -1 -1 1 2 -1 y x -1 1 -1 1 x 2 -1 1 2 1 -1 y 2 1 2 -1 2 1 -1 1 2 -1 y x -1 1 -1 1 x 2 -1 1 2 1 -1 y 2 1 2 -1 1 2 -1 1 -1 1 x 2 -1 1 2 -1 x -1 y 1 -1 y 2 1 2 2 -1 [/itex]

 Rule Form

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

 2007-05-02