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variants of this functions
ChebyshevU






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.05.21.0007.01









  


  










Input Form





Integrate[\[Nu]^(\[Alpha] - 1) ChebyshevU[\[Nu], z], \[Nu]] == ((-(\[Nu]^\[Alpha]/(2 Sqrt[1 - z^2]))) (((-I) z + Sqrt[1 - z^2]) Gamma[\[Alpha], \[Nu] (Im[ArcCos[z]] - I Re[ArcCos[z]])] ((-\[Nu]) (Im[ArcCos[z]] - I Re[ArcCos[z]]))^\[Alpha] + (I z + Sqrt[1 - z^2]) Gamma[\[Alpha], (-\[Nu]) (Im[ArcCos[z]] - I Re[ArcCos[z]])] (\[Nu] (Im[ArcCos[z]] - I Re[ArcCos[z]]))^ \[Alpha]))/((-\[Nu]^2) (Im[ArcCos[z]] - I Re[ArcCos[z]])^2)^\[Alpha]










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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