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variants of this functions
ArcTan






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTan[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > For the function itself





http://functions.wolfram.com/01.14.06.0021.01









  


  










Input Form





ArcTan[z] \[Proportional] ArcTan[Subscript[z, 0]] + (I/2) (Floor[Arg[I (Subscript[z, 0] - z)]/(2 Pi)] (Log[1 - I Subscript[z, 0]] + Log[1/(1 - I Subscript[z, 0])]) - Floor[Arg[I (z - Subscript[z, 0])]/(2 Pi)] (Log[1 + I Subscript[z, 0]] + Log[1/(1 + I Subscript[z, 0])])) + (1/(1 + Subscript[z, 0]^2)) (z - Subscript[z, 0]) - (Subscript[z, 0]/(1 + Subscript[z, 0]^2)^2) (z - Subscript[z, 0])^2 + O[(z - Subscript[z, 0])^3]










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[RowBox[List["ArcTan", "[", SubscriptBox["zz", "0"], "]"]], "+", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[SubscriptBox["zz", "0"], "-", "z"]], ")"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SubscriptBox["zz", "0"]]]]], "]"]], "+", RowBox[List["Log", "[", FractionBox["1", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SubscriptBox["zz", "0"]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]]]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SubscriptBox["zz", "0"]]]]], "]"]], "+", RowBox[List["Log", "[", FractionBox["1", RowBox[List["1", "+", RowBox[List["\[ImaginaryI]", " ", SubscriptBox["zz", "0"]]]]]], "]"]]]], ")"]]]]]], ")"]]]], "+", FractionBox[RowBox[List["z", "-", SubscriptBox["zz", "0"]]], RowBox[List["1", "+", SubsuperscriptBox["zz", "0", "2"]]]], "-", FractionBox[RowBox[List[SubscriptBox["zz", "0"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "2"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SubsuperscriptBox["zz", "0", "2"]]], ")"]], "2"]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], "]"]], "3"]]]]]]]










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





2007-05-02