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http://functions.wolfram.com/04.22.16.0008.01
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LucasL[m \[Nu]] == LucasL[m] LucasL[m (\[Nu] - 1)] -
(-1)^m LucasL[m (\[Nu] - 2)] /; Element[m, Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LucasL", "[", RowBox[List["m", " ", "\[Nu]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["LucasL", "[", "m", "]"]], RowBox[List["LucasL", "[", RowBox[List["m", RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], RowBox[List["LucasL", "[", RowBox[List["m", RowBox[List["(", RowBox[List["\[Nu]", "-", "2"]], ")"]]]], "]"]]]]]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]
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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> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> </msub> <mo>  </mo> <mrow> <mrow> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> m </mi> </msub> <mo> ⁢ </mo> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msub> </mrow> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> m </mi> </msup> <mo> ⁢ </mo> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </msub> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> LucasL </ci> <apply> <times /> <ci> m </ci> <ci> ν </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> LucasL </ci> <ci> m </ci> </apply> <apply> <ci> LucasL </ci> <apply> <times /> <ci> m </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <apply> <ci> LucasL </ci> <apply> <times /> <ci> m </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", RowBox[List["m_", " ", "\[Nu]_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["LucasL", "[", "m", "]"]], " ", RowBox[List["LucasL", "[", RowBox[List["m", " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", RowBox[List["LucasL", "[", RowBox[List["m", " ", RowBox[List["(", RowBox[List["\[Nu]", "-", "2"]], ")"]]]], "]"]]]]]], "/;", RowBox[List["m", "\[Element]", "Integers"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
