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variants of this functions
Fibonacci




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.06.26.0002.01









  


  








Input Form





Fibonacci[\[Nu], z] == (1 - UnitStep[-\[Nu]] DiscreteDelta[Sin[\[Nu] Pi]]) z^(\[Nu] - 1) HypergeometricPFQ[{(1 - \[Nu])/2, 1 - \[Nu]/2}, {1 - \[Nu]}, -(4/z^2)] - (1 - UnitStep[\[Nu]] DiscreteDelta[Sin[\[Nu] Pi]]) Cos[\[Nu] Pi] z^(-\[Nu] - 1) HypergeometricPFQ[{(1 + \[Nu])/2, 1 + \[Nu]/2}, {1 + \[Nu]}, -(4/z^2)] /; Re[z] > 0








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Fibonacci", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["-", "\[Nu]"]], "]"]], " ", RowBox[List["DiscreteDelta", "[", RowBox[List["Sin", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], "]"]]]]]], ")"]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "-", "1"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "\[Nu]"]], "}"]], ",", RowBox[List["-", FractionBox["4", SuperscriptBox["z", "2"]]]]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List[RowBox[List["UnitStep", "[", "\[Nu]", "]"]], " ", RowBox[List["DiscreteDelta", "[", RowBox[List["Sin", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], "]"]]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", "\[Nu]"]], "}"]], ",", RowBox[List["-", FractionBox["4", SuperscriptBox["z", "2"]]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]


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





2001-10-29