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variants of this functions
ArcTan




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[x,y] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/01.15.26.0004.01









  


  








Input Form





ArcTan[x, y] == (I/2) (1/(x Sqrt[1/x^2]) - 1) (Log[-y] - Log[y]) + ((Pi x)/(2 y)) Sqrt[y^2/x^2] - (x/y) Hypergeometric2F1[1/2, 1, 3/2, -(x^2/y^2)] /; Abs[y] > Abs[x] && Element[y, Reals]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", RowBox[List["x_", ",", "y_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[FractionBox["1", RowBox[List["x", " ", SqrtBox[FractionBox["1", SuperscriptBox["x", "2"]]]]]], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["-", "y"]], "]"]], "-", RowBox[List["Log", "[", "y", "]"]]]], ")"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Pi]", " ", "x"]], ")"]], " ", SqrtBox[FractionBox[SuperscriptBox["y", "2"], SuperscriptBox["x", "2"]]]]], RowBox[List["2", " ", "y"]]], "-", FractionBox[RowBox[List["x", " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", "1", ",", FractionBox["3", "2"], ",", RowBox[List["-", FractionBox[SuperscriptBox["x", "2"], SuperscriptBox["y", "2"]]]]]], "]"]]]], "y"]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "y", "]"]], ">", RowBox[List["Abs", "[", "x", "]"]]]], "&&", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]]]


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





2001-10-29