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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 z==infinity





http://functions.wolfram.com/07.06.06.0019.01









  


  








Input Form





Fibonacci[\[Nu], z] == ((1/z) (z Sin[(Pi \[Nu])/2]^2 - Sqrt[z^2] Cos[(Pi \[Nu])/2]^2) HypergeometricPFQ[{1 + \[Nu]/2, (1 + \[Nu])/2}, {1 + \[Nu]}, -(4/z^2)])/ (z^2)^((1 + \[Nu])/2) + (1/z) (z^2)^((\[Nu] - 1)/2) (z Sin[(Pi \[Nu])/2]^2 + Sqrt[z^2] Cos[(Pi \[Nu])/2]^2) HypergeometricPFQ[{1 - \[Nu]/2, (1 - \[Nu])/2}, {1 - \[Nu]}, -(4/z^2)] /; !IntervalMemberQ[Interval[{-2, 0}], I z] && !IntervalMemberQ[Interval[{0, 2}], I z] && !Element[\[Nu], Integers]








Standard Form





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MathML Form







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Rule Form





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





2001-10-29