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variants of this functions
ArcTan






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[z] > Transformations > Products, sums, and powers of the direct function > Differences of the direct function





http://functions.wolfram.com/01.14.16.0189.01









  


  










Input Form





ArcTan[x] - ArcTan[y] == (1/2) Pi ((-Sqrt[1/x^2]) x + Sqrt[1/y^2] y + ((x - y) Sqrt[(x y + 1)^2/(x - y)^2])/(x y + 1) + 1) + ArcCot[(x y + 1)/(x - y)] - Pi Floor[(-2 Arg[I/x - 1] + 2 Arg[1/x - 1/y] - 2 Arg[-1 - I/y] + 3 Pi)/ (4 Pi)] + Pi Floor[(-2 Arg[-1 - I/x] + 2 Arg[1/x - 1/y] - 2 Arg[I/y - 1] + Pi)/(4 Pi)]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcTan", "[", "x_", "]"]], "-", RowBox[List["ArcTan", "[", "y_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SqrtBox[FractionBox["1", SuperscriptBox["x", "2"]]]]], " ", "x"]], "+", RowBox[List[SqrtBox[FractionBox["1", SuperscriptBox["y", "2"]]], " ", "y"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["x", "-", "y"]], ")"]], " ", SqrtBox[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["x", " ", "y"]], "+", "1"]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["x", "-", "y"]], ")"]], "2"]]]]], RowBox[List[RowBox[List["x", " ", "y"]], "+", "1"]]], "+", "1"]], ")"]]]], "+", RowBox[List["ArcCot", "[", FractionBox[RowBox[List[RowBox[List["x", " ", "y"]], "+", "1"]], RowBox[List["x", "-", "y"]]], "]"]], "-", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Arg", "[", RowBox[List[FractionBox["\[ImaginaryI]", "x"], "-", "1"]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[FractionBox["1", "x"], "-", FractionBox["1", "y"]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "1"]], "-", FractionBox["\[ImaginaryI]", "y"]]], "]"]]]], "+", RowBox[List["3", " ", "\[Pi]"]]]], RowBox[List["4", " ", "\[Pi]"]]], "]"]]]], "+", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "1"]], "-", FractionBox["\[ImaginaryI]", "x"]]], "]"]]]], "+", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[FractionBox["1", "x"], "-", FractionBox["1", "y"]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["Arg", "[", RowBox[List[FractionBox["\[ImaginaryI]", "y"], "-", "1"]], "]"]]]], "+", "\[Pi]"]], RowBox[List["4", " ", "\[Pi]"]]], "]"]]]]]]]]]]










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





2007-05-02





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