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; }

 ArcTan

 http://functions.wolfram.com/01.14.16.0225.01

 Input Form

 ArcTan[x] + I ArcSech[y] == -ArcTan[(Sqrt[1 + x^2] Sqrt[1 - (I Sqrt[-1 + 1/y] Sqrt[1 + 1/y] + x/y)^2/ (1 + x^2)])/ ((-1)^Floor[1/2 - Arg[((-I) x Sqrt[-1 + 1/y] Sqrt[1 + 1/y] + 1/y)/ Sqrt[1 + x^2]]/Pi] (I Sqrt[-1 + 1/y] Sqrt[1 + 1/y] + x/y))] + (1/2) (-1)^(Floor[1/2 - Arg[((-I) x Sqrt[-1 + 1/y] Sqrt[1 + 1/y] + 1/y)/ Sqrt[1 + x^2]]/Pi] + Floor[1/2 - Arg[1 + x^2]/(2 Pi) + Arg[I Sqrt[-1 + 1/y] Sqrt[1 + 1/y] + x/y]/Pi]) Pi + (1/4) (1 + (-1)^(-Floor[-(Arg[1 - 1/y]/(2 Pi))])) Pi (-1 + (-1)^Floor[1/2 - Arg[(x Sqrt[1 - 1/y^2] + 1/y)/Sqrt[1 + x^2]]/Pi] + 2 (1 + (-1)^Floor[1/2 - Arg[(x Sqrt[1 - 1/y^2] + 1/y)/Sqrt[1 + x^2]]/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[(x Sqrt[1 - 1/y^2] + 1/y)/Sqrt[1 + x^2]]/ Pi]) Floor[1/2 - (Arg[(I - x)/Sqrt[1 + x^2]] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)]) - (1/4) (1 - (-1)^(-Floor[-(Arg[1 - 1/y]/(2 Pi))])) Pi (-1 + (-1)^Floor[1/2 - Arg[((-x) Sqrt[1 - 1/y^2] + 1/y)/Sqrt[1 + x^2]]/ Pi] + 2 (1 + (-1)^Floor[1/2 - Arg[((-x) Sqrt[1 - 1/y^2] + 1/y)/Sqrt[1 + x^2]]/ 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[((-x) Sqrt[1 - 1/y^2] + 1/y)/Sqrt[1 + x^2]]/ Pi]) Floor[1/2 - (Arg[(I + x)/Sqrt[1 + x^2]] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)])

 Standard Form

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"\[Pi]"]]]]], "]"]]]]]], ")"]]]]]]]]]]

 MathML Form

 tan - 1 ( x ) + sech - 1 ( y ) - tan - 1 ( ( - 1 ) - 1 2 - arg ( 1 y - x 1 y - 1 1 + 1 y x 2 + 1 ) π x 2 + 1 1 - ( 1 y - 1 1 + 1 y + x y ) 2 x 2 + 1 1 y - 1 1 + 1 y + x y ) + 1 4 ( 1 + ( - 1 ) - - arg ( 1 - 1 y ) 2 π ) π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 - 1 y 2 x + 1 y x 2 + 1 ) π ) arg ( - x x 2 + 1 ) + arg ( 1 - 1 y 2 + y ) 2 π + ( - 1 ) 1 2 - arg ( 1 - 1 y 2 x + 1 y x 2 + 1 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 - 1 y 2 x + 1 y x 2 + 1 ) π ) 1 2 - arg ( - x x 2 + 1 ) + arg ( 1 - 1 y 2 + y ) 2 π - 1 ) - 1 4 ( 1 - ( - 1 ) - - arg ( 1 - 1 y ) 2 π ) π ( 2 ( 1 + ( - 1 ) 1 2 - arg ( 1 y - x 1 - 1 y 2 x 2 + 1 ) π ) arg ( + x x 2 + 1 ) + arg ( 1 - 1 y 2 + y ) 2 π + ( - 1 ) 1 2 - arg ( 1 y - x 1 - 1 y 2 x 2 + 1 ) π - 2 ( - 1 + ( - 1 ) 1 2 - arg ( 1 y - x 1 - 1 y 2 x 2 + 1 ) π ) 1 2 - arg ( + x x 2 + 1 ) + arg ( 1 - 1 y 2 + y ) 2 π - 1 ) + 1 2 ( - 1 ) - arg ( x 2 + 1 ) 2 π + arg ( 1 y - 1 1 + 1 y + x y ) π + 1 2 + 1 2 - arg ( 1 y - x 1 y - 1 1 + 1 y x 2 + 1 ) π π x y -1 -1 -1 1 2 -1 1 y -1 -1 x 1 y -1 -1 1 2 1 1 y -1 1 2 x 2 1 1 2 -1 -1 x 2 1 1 2 1 -1 1 y -1 -1 1 2 1 1 y -1 1 2 x y -1 2 x 2 1 -1 1 2 1 y -1 -1 1 2 1 1 y -1 1 2 x y -1 -1 1 4 1 -1 -1 -1 1 -1 1 y -1 2 -1 2 1 -1 1 2 -1 1 -1 1 y 2 -1 1 2 x 1 y -1 x 2 1 1 2 -1 -1 -1 x x 2 1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 1 -1 1 y 2 -1 1 2 x 1 y -1 x 2 1 1 2 -1 -1 -1 2 -1 -1 1 2 -1 1 -1 1 y 2 -1 1 2 x 1 y -1 x 2 1 1 2 -1 -1 1 2 -1 -1 x x 2 1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 -1 1 4 1 -1 -1 -1 -1 1 -1 1 y -1 2 -1 2 1 -1 1 2 -1 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 x 2 1 1 2 -1 -1 x x 2 1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 x 2 1 1 2 -1 -1 -1 2 -1 -1 1 2 -1 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 x 2 1 1 2 -1 -1 1 2 -1 x x 2 1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 2 -1 -1 1 2 -1 -1 x 2 1 2 -1 1 y -1 -1 1 2 1 1 y -1 1 2 x y -1 -1 1 2 1 2 -1 1 y -1 -1 x 1 y -1 -1 1 2 1 1 y -1 1 2 x 2 1 1 2 -1 -1 [/itex]

 Rule Form

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

 2007-05-02