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 Fibonacci

 http://functions.wolfram.com/05.12.27.0003.01

 Input Form

 Fibonacci[n, z] == (-((2 I^(n + 1))/Sqrt[4 + z^2])) Sin[n ArcCos[-((I z)/2)]]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Fibonacci", "[", RowBox[List["n", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", SuperscriptBox["\[ImaginaryI]", RowBox[List["n", "+", "1"]]]]], SqrtBox[RowBox[List["4", "+", SuperscriptBox["z", "2"]]]]]]], " ", RowBox[List["Sin", "[", RowBox[List["n", " ", RowBox[List["ArcCos", "[", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"]]], "]"]]]], "]"]]]]]]]]

 MathML Form

 F TagBox["F", Fibonacci] n ( z ) - 2 n + 1 z 2 + 4 sin ( n cos - 1 ( - z 2 ) ) Fibonacci n z -1 2 n 1 z 2 4 1 2 -1 n -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox["\[ImaginaryI]", RowBox[List["n", "+", "1"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["n", " ", RowBox[List["ArcCos", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "z"]], ")"]]]], "]"]]]], "]"]]]], SqrtBox[RowBox[List["4", "+", SuperscriptBox["z", "2"]]]]]]]]]]]

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

 2001-10-29