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 Fibonacci

 http://functions.wolfram.com/04.11.03.0016.01

 Input Form

 Fibonacci[n] == (1/Sqrt[5]) (GoldenRatio^n - (1 - GoldenRatio)^n) /; Element[n, Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "n", "]"]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["5"]], RowBox[List["(", RowBox[List[SuperscriptBox["GoldenRatio", "n"], "-", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "GoldenRatio"]], ")"]], "n"]]], ")"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 F TagBox["F", Fibonacci] n ϕ TagBox["\[Phi]", Function[List[], GoldenRatio]] n - ( 1 - ϕ TagBox["\[Phi]", Function[List[], GoldenRatio]] ) n 5 /; n TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] Condition Fibonacci n GoldenRatio n -1 1 -1 GoldenRatio n 5 1 2 -1 n [/itex]

 Rule Form

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

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

 2007-05-02