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 LucasL

 http://functions.wolfram.com/04.22.16.0006.01

 Input Form

 LucasL[2 n] == (1/2) (5 Fibonacci[n]^2 + LucasL[n]^2) /; Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["LucasL", "[", RowBox[List["2", "n"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["5", SuperscriptBox[RowBox[List["Fibonacci", "[", "n", "]"]], "2"]]], "+", SuperscriptBox[RowBox[List["LucasL", "[", "n", "]"]], "2"]]], ")"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 L TagBox["L", LucasL] 2 n 1 2 ( 5 F TagBox["F", Fibonacci] n 2 + L TagBox["L", LucasL] n 2 ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] Condition LucasL 2 n 1 2 5 Fibonacci n 2 LucasL n 2 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["LucasL", "[", RowBox[List["2", " ", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox[RowBox[List["Fibonacci", "[", "n", "]"]], "2"]]], "+", SuperscriptBox[RowBox[List["LucasL", "[", "n", "]"]], "2"]]], ")"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

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

 2007-05-02