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/01.17.16.0194.01

 Input Form

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

 Standard Form

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

 MathML Form

 a csc - 1 ( x ) + b sin - 1 ( y ) - 2 π ( - arg ( ( 1 - 1 x 2 + x ) - a ) - arg ( ( y + 1 - y 2 ) - b ) + π 2 π + Re ( a log ( 1 - 1 x 2 + x ) ) + π 2 π + Re ( b log ( y + 1 - y 2 ) ) + π 2 π ) + ( 1 - ( - 1 ) - arg ( ( y + 1 - y 2 ) - b ( 1 - 1 x 2 + x ) - a + 1 ) 2 π - - arg ( ( 1 - 1 x 2 + x ) - a ( y + 1 - y 2 ) - b ) 2 π ) π + ( - 1 ) - arg ( ( 1 - 1 x 2 + x ) - a ( y + 1 - y 2 ) - b ) π + arg ( ( 1 - 1 x 2 + x ) - a ( y + 1 - y 2 ) - b - 1 ) 2 π + 1 2 - arg ( ( y + 1 - y 2 ) - b ( 1 - 1 x 2 + x ) - a + 1 ) 2 π ( csc - 1 ( 2 ( 1 - 1 x 2 + x ) - a ( y + 1 - y 2 ) - b ( y + 1 - y 2 ) - 2 b ( 1 - 1 x 2 + x ) - 2 a + 1 ) - π 2 ) a x b y -2 -1 1 -1 1 x 2 -1 1 2 x -1 -1 a -1 y 1 -1 y 2 1 2 -1 b 2 -1 a 1 -1 1 x 2 -1 1 2 x -1 2 -1 b y 1 -1 y 2 1 2 2 -1 1 -1 -1 -1 y 1 -1 y 2 1 2 -1 b 1 -1 1 x 2 -1 1 2 x -1 -1 a 1 2 -1 -1 -1 1 -1 1 x 2 -1 1 2 x -1 -1 a y 1 -1 y 2 1 2 -1 b 2 -1 -1 -1 1 -1 1 x 2 -1 1 2 x -1 -1 a y 1 -1 y 2 1 2 -1 b -1 1 -1 1 x 2 -1 1 2 x -1 -1 a y 1 -1 y 2 1 2 -1 b -1 2 -1 1 2 -1 y 1 -1 y 2 1 2 -1 b 1 -1 1 x 2 -1 1 2 x -1 -1 a 1 2 -1 2 1 -1 1 x 2 -1 1 2 x -1 -1 a y 1 -1 y 2 1 2 -1 b y 1 -1 y 2 1 2 -2 b 1 -1 1 x 2 -1 1 2 x -1 -2 a 1 -1 -1 2 -1 [/itex]

 Rule Form

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

 2007-05-02