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variants of this functions
ArcTan






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[z] > Continued fraction representations





http://functions.wolfram.com/01.14.10.0005.01









  


  










Input Form





ArcTan[z] == z/(1 + z^2 - (2 z^2)/(3 - (2 z^2)/(5 (1 + z^2) - (12 z^2)/(7 - (12 z^2)/(9 (1 + z^2) - (30 z^2)/ (11 - (30 z^2)/(13 (1 + z^2) - \[Ellipsis]))))))) /; !IntervalMemberQ[Interval[{-Infinity, -1}], I z] && !IntervalMemberQ[Interval[{1, Infinity}], I z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["ArcTan", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["z", RowBox[List["1", "+", SuperscriptBox["z", "2"], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", "2"]]], RowBox[List["3", "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", "2"]]], RowBox[List[RowBox[List["5", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]]]], "-", FractionBox[RowBox[List["12", " ", SuperscriptBox["z", "2"]]], RowBox[List["7", "-", FractionBox[RowBox[List["12", " ", SuperscriptBox["z", "2"]]], RowBox[List[RowBox[List["9", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]]]], "-", FractionBox[RowBox[List["30", " ", SuperscriptBox["z", "2"]]], RowBox[List["11", "-", FractionBox[RowBox[List["30", " ", SuperscriptBox["z", "2"]]], RowBox[List[RowBox[List["13", " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["z", "2"]]], ")"]]]], "-", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]]]]










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





2001-10-29