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variants of this functions
ArcTan




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[z] > Series representations > Generalized power series > Expansions at z==infinity > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.14.06.0066.01









  


  








Input Form





ArcTan[z]^2 == Pi^2/4 + (1/z^2) Hypergeometric2F1[1/2, 1, 3/2, -(1/z^2)]^2 - (Pi/Sqrt[z^2]) Hypergeometric2F1[1/2, 1, 3/2, -(1/z^2)] /; !IntervalMemberQ[Interval[{-1, 1}], I z]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["ArcTan", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[SuperscriptBox["\[Pi]", "2"], "4"], "+", FractionBox[SuperscriptBox[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", "1", ",", FractionBox["3", "2"], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]], "2"], SuperscriptBox["z", "2"]], "-", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["1", "2"], ",", "1", ",", FractionBox["3", "2"], ",", RowBox[List["-", FractionBox["1", SuperscriptBox["z", "2"]]]]]], "]"]]]], SqrtBox[SuperscriptBox["z", "2"]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "1"]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]]


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





2007-05-02