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 Fibonacci

 http://functions.wolfram.com/04.11.26.0025.01

 Input Form

 Fibonacci[n] == I^(n - 1) ChebyshevU[n - 1, -(I/2)] /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "n", "]"]], "\[Equal]", RowBox[List[SuperscriptBox["\[ImaginaryI]", RowBox[List["n", "-", "1"]]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", RowBox[List["-", FractionBox["\[ImaginaryI]", "2"]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 F TagBox["F", Fibonacci] n n - 1 U n - 1 ( - 2 ) /; n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] Condition Fibonacci n n -1 ChebyshevU n -1 -1 2 -1 n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ImaginaryI]", RowBox[List["n", "-", "1"]]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["n", "-", "1"]], ",", RowBox[List["-", FractionBox["\[ImaginaryI]", "2"]]]]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.