Lucas numbers: Transformations (formula 04.22.16.0013)

LucasL

$Mathematica Notation$

Integer Functions

LucasL[nu]

Transformations

Products, sums, and powers of the direct function

Products of the direct function

http://functions.wolfram.com/04.22.16.0013.01

Input Form

LucasL[\[Nu] + 1] LucasL[\[Nu] - 1] == LucasL[\[Nu]]^2 - 5 Cos[Pi \[Nu]]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]], " ", RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "-", "1"]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["LucasL", "[", "\[Nu]", "]"]], "2"], "-", RowBox[List["5", " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]]]]]]

MathML Form

<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> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <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> </mrow> <mo>  </mo> <mrow> <msubsup> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox["L", LucasL] </annotation> </semantics> <mi> ν </mi> <mn> 2 </mn> </msubsup> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> LucasL </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> LucasL </ci> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <ci> LucasL </ci> <ci> ν </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <cos /> <apply> <times /> <pi /> <ci> ν </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["LucasL", "[", RowBox[List["\[Nu]_", "+", "1"]], "]"]], " ", RowBox[List["LucasL", "[", RowBox[List["\[Nu]_", "-", "1"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["LucasL", "[", "\[Nu]", "]"]], "2"], "-", RowBox[List["5", " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]]]]]]

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

2007-05-02