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http://functions.wolfram.com/04.22.16.0004.01
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LucasL[2 \[Nu]] == (1/5) (3 LucasL[\[Nu]]^2 -
2 LucasL[\[Nu]] LucasL[1 + \[Nu]] + 2 LucasL[1 + \[Nu]]^2 -
(5 Sin[Pi \[Nu]]^2)/GoldenRatio^(2 \[Nu]))
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Cell[BoxData[RowBox[List[RowBox[List["LucasL", "[", RowBox[List["2", " ", "\[Nu]"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "5"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List["LucasL", "[", "\[Nu]", "]"]], "2"]]], "-", RowBox[List["2", " ", RowBox[List["LucasL", "[", "\[Nu]", "]"]], " ", RowBox[List["LucasL", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["LucasL", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]], "2"]]], "-", RowBox[List["5", " ", SuperscriptBox["GoldenRatio", RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"]]]]], ")"]]]]]]]]
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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> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msub> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 5 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <msubsup> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> ν </mi> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> ⁢ </mo> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> ν </mi> </msub> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msubsup> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <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> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LucasL </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 5 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <ci> LucasL </ci> <ci> ν </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> LucasL </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> LucasL </ci> <ci> ν </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <ci> LucasL </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <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> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", RowBox[List["2", " ", "\[Nu]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "5"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox[RowBox[List["LucasL", "[", "\[Nu]", "]"]], "2"]]], "-", RowBox[List["2", " ", RowBox[List["LucasL", "[", "\[Nu]", "]"]], " ", RowBox[List["LucasL", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]]], "+", RowBox[List["2", " ", SuperscriptBox[RowBox[List["LucasL", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]], "2"]]], "-", RowBox[List["5", " ", SuperscriptBox["GoldenRatio", RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], "2"]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
