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/01.14.16.0203.01

 Input Form

 ArcTan[x] + ArcSec[y] == Pi/2 + ((Sqrt[1 + x^2] Sqrt[((-x) Sqrt[1 - 1/y^2] + 1/y)^2/(1 + x^2)])/ ((-x) Sqrt[1 - 1/y^2] + 1/y)) ArcSin[(Sqrt[1 - 1/y^2] + x/y)/ Sqrt[1 + x^2]] - (Pi Sqrt[1 + x^2] Sqrt[((-x) Sqrt[1 - 1/y^2] + 1/y)^2/(1 + x^2)])/ (2 ((-x) Sqrt[1 - 1/y^2] + 1/y)) - Pi (1 + (Sqrt[1 + x^2] Sqrt[((-x) Sqrt[1 - 1/y^2] + 1/y)^2/(1 + x^2)])/ ((-x) Sqrt[1 - 1/y^2] + 1/y)) Floor[(Arg[(I + x)/Sqrt[1 + x^2]] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)] + Pi (-1 + (Sqrt[1 + x^2] Sqrt[((-x) Sqrt[1 - 1/y^2] + 1/y)^2/(1 + x^2)])/ ((-x) Sqrt[1 - 1/y^2] + 1/y)) Floor[-((-Pi + 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["ArcTan", "[", "x", "]"]], "+", RowBox[List["ArcSec", "[", "y", "]"]]]], "\[Equal]", RowBox[List[FractionBox["\[Pi]", "2"], "+", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]]], " ", RowBox[List["ArcSin", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["x", "y"]]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]], "]"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]]]]], "-", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]]]]], ")"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["Arg", "[", FractionBox[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]"]]], "]"]]]], "+", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]]]]], ")"]], " ", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["-", "\[Pi]"]], "+", RowBox[List["Arg", "[", FractionBox[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

 tan - 1 ( x ) + sec - 1 ( y ) π 2 + ( 1 y - x 1 - 1 y 2 ) 2 x 2 + 1 x 2 + 1 1 y - x 1 - 1 y 2 sin - 1 ( x y + 1 - 1 y 2 x 2 + 1 ) - π ( ( 1 y - x 1 - 1 y 2 ) 2 x 2 + 1 x 2 + 1 1 y - x 1 - 1 y 2 + 1 ) arg ( + x x 2 + 1 ) + arg ( 1 - 1 y 2 + y ) 2 π + π ( x 2 + 1 ( 1 y - x 1 - 1 y 2 ) 2 x 2 + 1 1 y - x 1 - 1 y 2 - 1 ) - arg ( + x x 2 + 1 ) + arg ( 1 - 1 y 2 + y ) - π 2 π - π x 2 + 1 ( 1 y - x 1 - 1 y 2 ) 2 x 2 + 1 2 ( 1 y - x 1 - 1 y 2 ) x y 2 -1 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 2 x 2 1 -1 1 2 x 2 1 1 2 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 -1 x y -1 1 -1 1 y 2 -1 1 2 x 2 1 1 2 -1 -1 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 2 x 2 1 -1 1 2 x 2 1 1 2 1 y -1 -1 x 1 -1 1 y 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 x 2 1 1 2 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 2 x 2 1 -1 1 2 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 -1 -1 -1 x x 2 1 1 2 -1 1 -1 1 y 2 -1 1 2 y -1 -1 2 -1 -1 x 2 1 1 2 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 2 x 2 1 -1 1 2 2 1 y -1 -1 x 1 -1 1 y 2 -1 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcTan", "[", "x_", "]"]], "+", RowBox[List["ArcSec", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["\[Pi]", "2"], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], ")"]], " ", RowBox[List["ArcSin", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]], "+", FractionBox["x", "y"]]], SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]], "]"]]]], RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]]], "-", FractionBox[RowBox[List["\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]]]]], "-", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]]]]], ")"]], " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List["Arg", "[", FractionBox[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]"]]], "]"]]]], "+", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "+", SuperscriptBox["x", "2"]]]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]], ")"]], "2"], RowBox[List["1", "+", SuperscriptBox["x", "2"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "x"]], " ", SqrtBox[RowBox[List["1", "-", FractionBox["1", SuperscriptBox["y", "2"]]]]]]], "+", FractionBox["1", "y"]]]]]], ")"]], " ", RowBox[List["Floor", "[", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["-", "\[Pi]"]], "+", RowBox[List["Arg", "[", FractionBox[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]"]]]]], "]"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02