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variants of this functions
Fibonacci




Mathematica Notation

Traditional Notation









Integer Functions > Fibonacci[nu] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/04.11.26.0013.01









  


  








Input Form





Fibonacci[n] == (n/2)^(n - 2 Floor[(n - 1)/2] - 1) HypergeometricPFQ[{-Floor[(n - 1)/2], 1 + Floor[n/2]}, {1 + (-1)^n/2}, -(1/4)] /; Element[n, Integers]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "n", "]"]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["n", "2"], ")"]], RowBox[List["n", "-", RowBox[List["2", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], "-", "1"]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], ",", RowBox[List["1", "+", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "2"]]], "}"]], ",", RowBox[List["-", FractionBox["1", "4"]]]]], "]"]]]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["n", "2"], ")"]], RowBox[List["n", "-", RowBox[List["2", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], "-", "1"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], ",", RowBox[List["1", "+", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], "2"]]], "}"]], ",", RowBox[List["-", FractionBox["1", "4"]]]]], "]"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]


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





2001-10-29