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LucasL




Mathematica Notation

Traditional Notation









Integer Functions > LucasL[nu] > Identities > Recurrence identities > Consecutive neighbors





http://functions.wolfram.com/04.22.17.0003.01









  


  








Input Form





LucasL[\[Nu]] == (LucasL[\[Nu] + 1] - Sqrt[5] GoldenRatio^\[Nu])/ (1 - GoldenRatio)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["LucasL", "[", "\[Nu]", "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]], "-", RowBox[List[SqrtBox["5"], SuperscriptBox["GoldenRatio", "\[Nu]"]]]]], RowBox[List["1", "-", "GoldenRatio"]]]]]]]








MathML Form







<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[&quot;L&quot;, LucasL] </annotation> </semantics> <mi> &#957; </mi> </msub> <mo> &#63449; </mo> <mfrac> <mrow> <msub> <semantics> <mi> L </mi> <annotation encoding='Mathematica'> TagBox[&quot;L&quot;, LucasL] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msub> <mo> - </mo> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> &#8290; </mo> <msup> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> <mi> &#957; </mi> </msup> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[List[], GoldenRatio]] </annotation> </semantics> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LucasL </ci> <ci> &#957; </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> LucasL </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> GoldenRatio </ci> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> GoldenRatio </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", "\[Nu]_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]], "-", RowBox[List[SqrtBox["5"], " ", SuperscriptBox["GoldenRatio", "\[Nu]"]]]]], RowBox[List["1", "-", "GoldenRatio"]]]]]]]


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





2007-05-02