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http://functions.wolfram.com/04.11.06.0004.01
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Fibonacci[\[Nu]] \[Proportional] (1/Sqrt[5]) (GoldenRatio^\[Nu] -
Cos[\[Nu] Pi]/GoldenRatio^\[Nu]) /; (Abs[\[Nu]] -> Infinity)
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "\[Nu]", "]"]], "\[Proportional]", RowBox[List[FractionBox["1", SqrtBox["5"]], RowBox[List["(", RowBox[List[SuperscriptBox["GoldenRatio", "\[Nu]"], "-", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], " ", SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]]]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mi> ν </mi> </msub> <mo> ∝ </mo> <mfrac> <mrow> <msup> <mi> ϕ </mi> <mi> ν </mi> </msup> <mo> - </mo> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[GoldenRatio]] </annotation> </semantics> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msup> </mrow> </mrow> <msqrt> <mn> 5 </mn> </msqrt> </mfrac> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> ν </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Fibonacci </ci> <ci> ν </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> ϕ </ci> <ci> ν </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <cos /> <apply> <times /> <ci> ν </ci> <pi /> </apply> </apply> <apply> <power /> <ci> GoldenRatio </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> ν </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", "\[Nu]_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["GoldenRatio", "\[Nu]"], "-", RowBox[List[RowBox[List["Cos", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], " ", SuperscriptBox["GoldenRatio", RowBox[List["-", "\[Nu]"]]]]]]], SqrtBox["5"]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
