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variants of this functions
Fibonacci






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Fibonacci[nu,z] > Series representations > Generalized power series > Expansions at generic point nu==nu0 > For the function itself





http://functions.wolfram.com/07.06.06.0029.01









  


  










Input Form





Fibonacci[\[Nu], z] \[Proportional] Fibonacci[Subscript[\[Nu], 0], z] + ((1/Sqrt[4 + z^2]) ((ArcSinh[z/2] ((z + Sqrt[4 + z^2])^(2 Subscript[\[Nu], 0]) + 4^Subscript[\[Nu], 0] Cos[Pi Subscript[\[Nu], 0]]) + 4^Subscript[\[Nu], 0] Pi Sin[Pi Subscript[\[Nu], 0]])/ (2^Subscript[\[Nu], 0] (z + Sqrt[4 + z^2])^Subscript[\[Nu], 0]))) (\[Nu] - Subscript[\[Nu], 0]) + (1/2) (ArcSinh[z/2]^2 Fibonacci[Subscript[\[Nu], 0], z] + (1/Sqrt[4 + z^2]) ((2^Subscript[\[Nu], 0] Pi (Pi Cos[Pi Subscript[\[Nu], 0]] - 2 ArcSinh[z/2] Sin[Pi Subscript[\[Nu], 0]]))/(z + Sqrt[4 + z^2])^ Subscript[\[Nu], 0])) (\[Nu] - Subscript[\[Nu], 0])^2 + O[(\[Nu] - Subscript[\[Nu], 0])^3]










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["Fibonacci", "[", RowBox[List[SubscriptBox["\[Nu]\[Nu]", "0"], ",", "z"]], "]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", SubscriptBox["\[Nu]\[Nu]", "0"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", SqrtBox[RowBox[List["4", "+", SuperscriptBox["z", "2"]]]]]], ")"]], RowBox[List["-", SubscriptBox["\[Nu]\[Nu]", "0"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["ArcSinh", "[", FractionBox["z", "2"], "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", SqrtBox[RowBox[List["4", "+", SuperscriptBox["z", "2"]]]]]], ")"]], RowBox[List["2", " ", SubscriptBox["\[Nu]\[Nu]", "0"]]]], "+", RowBox[List[SuperscriptBox["4", SubscriptBox["\[Nu]\[Nu]", "0"]], " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["4", SubscriptBox["\[Nu]\[Nu]", "0"]], " ", "\[Pi]", " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]]]]]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ")"]]]], SqrtBox[RowBox[List["4", "+", SuperscriptBox["z", "2"]]]]], "+", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["ArcSinh", "[", FractionBox["z", "2"], "]"]], "2"], " ", RowBox[List["Fibonacci", "[", RowBox[List[SubscriptBox["\[Nu]\[Nu]", "0"], ",", "z"]], "]"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["2", SubscriptBox["\[Nu]\[Nu]", "0"]], " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", SqrtBox[RowBox[List["4", "+", SuperscriptBox["z", "2"]]]]]], ")"]], RowBox[List["-", SubscriptBox["\[Nu]\[Nu]", "0"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["Cos", "[", RowBox[List["\[Pi]", " ", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["ArcSinh", "[", FractionBox["z", "2"], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]]]]]], ")"]]]], SqrtBox[RowBox[List["4", "+", SuperscriptBox["z", "2"]]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], ")"]], "2"]]], "+", SuperscriptBox[RowBox[List["O", "[", RowBox[List["\[Nu]", "-", SubscriptBox["\[Nu]\[Nu]", "0"]]], "]"]], "3"]]]]]]]










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





2007-05-02





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