Lucas numbers: Transformations (formula 04.22.16.0019)

LucasL

$Mathematica Notation$

Integer Functions

LucasL[nu]

Transformations

Products, sums, and powers of the direct function

Powers of the direct function

http://functions.wolfram.com/04.22.16.0019.01

Input Form

LucasL[n]^5 == LucasL[5 n] + 5 (-1)^n LucasL[3 n] + 10 LucasL[n] /; Element[n, Integers]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["LucasL", "[", "n", "]"]], "5"], "\[Equal]", RowBox[List[RowBox[List["LucasL", "[", RowBox[List["5", " ", "n"]], "]"]], "+", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["LucasL", "[", RowBox[List["3", " ", "n"]], "]"]]]], "+", RowBox[List["10", " ", RowBox[List["LucasL", "[", "n", "]"]]]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> n </mi> <mn> 5 </mn> </msubsup> <mo>  </mo> <mrow> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> </msub> <mo> + </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> ⁢ </mo> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> n </mi> </mrow> </msub> </mrow> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> ⁢ </mo> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> n </mi> </msub> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </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> <power /> <apply> <ci> LucasL </ci> <ci> n </ci> </apply> <cn type='integer'> 5 </cn> </apply> <apply> <plus /> <apply> <ci> LucasL </ci> <apply> <times /> <cn type='integer'> 5 </cn> <ci> n </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <ci> LucasL </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <ci> LucasL </ci> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["LucasL", "[", "n_", "]"]], "5"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["LucasL", "[", RowBox[List["5", " ", "n"]], "]"]], "+", RowBox[List["5", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["LucasL", "[", RowBox[List["3", " ", "n"]], "]"]]]], "+", RowBox[List["10", " ", RowBox[List["LucasL", "[", "n", "]"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

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

2007-05-02