|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/04.11.16.0026.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Fibonacci[\[Nu]] == (1/5) (LucasL[\[Nu] - 1] + LucasL[\[Nu] + 1])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Fibonacci", "[", "\[Nu]", "]"]], "\[Equal]", RowBox[List[FractionBox["1", "5"], " ", RowBox[List["(", RowBox[List[RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "-", "1"]], "]"]], "+", RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]]], ")"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox["F", Fibonacci] </annotation> </semantics> <mi> ν </mi> </msub> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 5 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <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> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Fibonacci </ci> <ci> ν </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 5 </cn> <apply> <plus /> <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> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", "\[Nu]_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "5"], " ", RowBox[List["(", RowBox[List[RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "-", "1"]], "]"]], "+", RowBox[List["LucasL", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|