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variants of this functions
Fibonacci






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Fibonacci[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions with respect to nu > Involving power function





http://functions.wolfram.com/07.06.21.0005.01









  


  










Input Form





Integrate[\[Nu]^(\[Alpha] - 1) Fibonacci[\[Nu], z], \[Nu]] == (1/(2 Sqrt[4 + z^2])) (\[Nu]^\[Alpha] ((-2 Gamma[\[Alpha], (-\[Nu]) Log[(1/2) (z + Sqrt[4 + z^2])]])/ ((-\[Nu]) Log[(1/2) (z + Sqrt[4 + z^2])])^\[Alpha] + Gamma[\[Alpha], \[Nu] ((-I) Pi + Log[(1/2) (z + Sqrt[4 + z^2])])]/ (\[Nu] ((-I) Pi + Log[(1/2) (z + Sqrt[4 + z^2])]))^\[Alpha] + Gamma[\[Alpha], \[Nu] (I Pi + Log[(1/2) (z + Sqrt[4 + z^2])])]/ (\[Nu] (I Pi + Log[(1/2) (z + Sqrt[4 + z^2])]))^\[Alpha]))










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