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; }

 ArcCos

 http://functions.wolfram.com/01.13.16.0200.01

 Input Form

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

 Standard Form

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

 MathML Form

 cos - 1 ( x ) - sech - 1 ( y ) cos - 1 ( ( - 1 ) 1 2 - arg ( 1 - x 2 1 y - 1 1 + 1 y + x y ) π ( x 1 y - 1 1 + 1 y - 1 - x 2 y ) ) - 1 2 π ( 1 2 ( 1 - ( - 1 ) - - arg ( 1 - 1 y ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( x y + 1 - x 2 1 - 1 y 2 ) π ) arg ( 1 - x 2 - x ) + arg ( 1 - 1 y 2 + y ) 2 π + ( - 1 ) 1 2 - arg ( x y + 1 - x 2 1 - 1 y 2 ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( x y + 1 - x 2 1 - 1 y 2 ) π ) 1 2 - arg ( 1 - x 2 - x ) + arg ( 1 - 1 y 2 + y ) 2 π ) - 1 2 ( 1 + ( - 1 ) - - arg ( 1 - 1 y ) 2 π ) ( 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 - x 2 1 - 1 y 2 - x y ) π ) arg ( x + 1 - x 2 ) + arg ( 1 - 1 y 2 + y ) 2 π + ( - 1 ) 1 2 - arg ( 1 - x 2 1 - 1 y 2 - x y ) π + 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 - x 2 1 - 1 y 2 - x y ) π ) 1 2 - arg ( x + 1 - x 2 ) + arg ( 1 - 1 y 2 + y ) 2 π ) ) x -1 y -1 1 2 -1 1 -1 x 2 1 2 1 y -1 -1 1 2 1 1 y -1 1 2 x y -1 -1 x 1 y -1 -1 1 2 1 1 y -1 1 2 -1 1 -1 x 2 1 2 y -1 -1 1 2 1 2 1 -1 -1 -1 -1 1 -1 1 y -1 2 -1 2 -1 -1 1 2 -1 x y -1 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 -1 1 -1 x 2 1 2 -1 x 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 x y -1 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 -1 2 1 -1 1 2 -1 x y -1 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 -1 1 2 -1 1 -1 x 2 1 2 -1 x 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 1 -1 -1 -1 1 -1 1 y -1 2 -1 2 -1 -1 1 2 -1 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 -1 x y -1 -1 x 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 -1 x y -1 -1 2 1 -1 1 2 -1 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 -1 x y -1 -1 1 2 -1 x 1 -1 x 2 1 2 1 -1 1 y 2 -1 1 2 y -1 2 -1 [/itex]

 Rule Form

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

 2007-05-02