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/05.12.06.0005.01

 Input Form

 Fibonacci[n, z] == Sum[Binomial[n - k - 1, k] z^(n - 2 k - 1), {k, 0, Floor[(n - 1)/2]}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Fibonacci", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "-", "k", "-", "1"]], ",", "k"]], "]"]], " ", SuperscriptBox["z", RowBox[List["n", "-", RowBox[List["2", " ", "k"]], "-", "1"]]]]]]]]]]]

 MathML Form

 F TagBox["F", Fibonacci] n ( z ) k = 0 n - 1 2 ( n - k - 1 k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox[RowBox[List["n", "-", "k", "-", "1"]], Identity, Rule[Editable, True]]], List[TagBox["k", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] z n - 2 k - 1 Fibonacci n z k 0 n -1 2 -1 Binomial n -1 k -1 k z n -1 2 k -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List[RowBox[List["n", "-", "k", "-", "1"]], ",", "k"]], "]"]], " ", SuperscriptBox["z", RowBox[List["n", "-", RowBox[List["2", " ", "k"]], "-", "1"]]]]]]]]]]]

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

 2001-10-29