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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==-i > For small integer powers of the function > For the second power





http://functions.wolfram.com/01.14.06.0053.01









  


  








Input Form





ArcTan[z]^2 \[Proportional] (-(1/4)) Log[-((I (z + I))/2)]^2 + ((z + I)^2/16) (1 - (I/2) (z + I) - (11/48) (z + I)^2 + \[Ellipsis]) + (I/4) Log[-((I (z + I))/2)] (z + I) (1 - (I/4) (z + I) - (1/12) (z + I)^2 + \[Ellipsis]) /; (z -> -I)








Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 16 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <imaginaryi /> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <ci> z </ci> <imaginaryi /> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 11 <sep /> 48 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <imaginaryi /> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["ArcTan", "[", "z_", "]"]], "2"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", SuperscriptBox[RowBox[List["Log", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]], ")"]]]], "]"]], "2"]]], "+", RowBox[List[FractionBox["1", "16"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]], "2"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]], "-", RowBox[List[FractionBox["11", "48"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]], "2"]]], "+", "\[Ellipsis]"]], ")"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]], ")"]]]], "]"]], " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]]]], "-", RowBox[List[FractionBox["1", "12"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "\[ImaginaryI]"]], ")"]], "2"]]], "+", "\[Ellipsis]"]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", RowBox[List["-", "\[ImaginaryI]"]]]], ")"]]]]]]]]


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





2007-05-02