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 Fibonacci

 http://functions.wolfram.com/04.11.03.0017.01

 Input Form

 Fibonacci[n + 1] == Floor[(1 + (1 + Sqrt[5]) Fibonacci[n])/2] /; Element[n, Integers] && n > 1

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", RowBox[List["n", "+", "1"]], "]"]], "\[Equal]", RowBox[List["Floor", "[", FractionBox[RowBox[List["1", "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", SqrtBox["5"]]], ")"]], RowBox[List["Fibonacci", "[", "n", "]"]]]]]], "2"], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "1"]]]]]]]]

 MathML Form

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

 Rule Form

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

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

 2007-05-02