html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Fibonacci

 http://functions.wolfram.com/04.11.03.0001.01

 Input Form

 Fibonacci[n] == (1/Sqrt[5]) (((1 + Sqrt[5])/2)^n - ((1 - Sqrt[5])/2)^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[RowBox[List["(", FractionBox[RowBox[List["1", "+", SqrtBox["5"]]], "2"], ")"]], "n"], "-", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["1", "-", SqrtBox["5"]]], "2"], ")"]], "n"]]], ")"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

 MathML Form

 F TagBox["F", Fibonacci] n 1 5 ( ( 1 + 5 2 ) n - ( 1 - 5 2 ) n ) /; n Condition Fibonacci n 1 5 1 2 -1 1 5 1 2 2 -1 n -1 1 -1 5 1 2 2 -1 n n [/itex]

 Rule Form

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

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

 2001-10-29