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http://functions.wolfram.com/04.22.27.0007.01
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LucasL[\[Nu]] == Fibonacci[2 \[Nu]]/Fibonacci[\[Nu]] -
Sin[Pi \[Nu]]^2/(GoldenRatio^(2 \[Nu]) (Sqrt[5] Fibonacci[\[Nu]]))
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Cell[BoxData[RowBox[List[RowBox[List["LucasL", "[", "\[Nu]", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["Fibonacci", "[", RowBox[List["2", "\[Nu]"]], "]"]], RowBox[List["Fibonacci", "[", "\[Nu]", "]"]]], "-", FractionBox[RowBox[List[SuperscriptBox["GoldenRatio", RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"]]], RowBox[List[SqrtBox["5"], RowBox[List["Fibonacci", "[", "\[Nu]", "]"]]]]]]]]]]]
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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> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> ν </mi> </msub> <mo>  </mo> <mrow> <mfrac> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msub> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mi> ν </mi> </msub> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <semantics> <mi> ϕ </mi> <annotation encoding='Mathematica'> TagBox["\[Phi]", Function[List[], GoldenRatio]] </annotation> </semantics> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> ⁢ </mo> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mi> ν </mi> </msub> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LucasL </ci> <ci> ν </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Fibonacci </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> <apply> <power /> <apply> <ci> Fibonacci </ci> <ci> ν </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> GoldenRatio </ci> <apply> <times /> <cn type='integer'> -2 </cn> <ci> ν </ci> </apply> </apply> <apply> <power /> <apply> <sin /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Fibonacci </ci> <ci> ν </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", "\[Nu]_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["Fibonacci", "[", RowBox[List["2", " ", "\[Nu]"]], "]"]], RowBox[List["Fibonacci", "[", "\[Nu]", "]"]]], "-", FractionBox[RowBox[List[SuperscriptBox["GoldenRatio", RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"]]], RowBox[List[SqrtBox["5"], " ", RowBox[List["Fibonacci", "[", "\[Nu]", "]"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
