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variants of this functions
Fibonacci




Mathematica Notation

Traditional Notation









Polynomials > Fibonacci[n,z] > Series representations > Generalized power series > Expansions at z==-2i





http://functions.wolfram.com/05.12.06.0013.01









  


  








Input Form





Fibonacci[n, z] \[Proportional] (-n) (-I)^(n + 1) (1 + O[z + 2 I]) /; (z -> -2 I)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", "n"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], RowBox[List["n", "+", "1"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", RowBox[List["2", "\[ImaginaryI]"]]]], "]"]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", RowBox[List[RowBox[List["-", "2"]], "\[ImaginaryI]"]]]], ")"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox[&quot;F&quot;, Fibonacci] </annotation> </semantics> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mrow> <mo> - </mo> <mi> n </mi> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Fibonacci </ci> <ci> n </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "n"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "\[ImaginaryI]"]], ")"]], RowBox[List["n", "+", "1"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], "]"]]]], ")"]]]], "/;", RowBox[List["(", RowBox[List["z", "\[Rule]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]"]]]], ")"]]]]]]]]


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





2001-10-29