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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Integration > Indefinite integration > Involving direct function and Bessel-type functions > Involving Bessel functions > Involving Bessel J and power > Linear arguments





http://functions.wolfram.com/03.03.21.0099.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) (a BesselJ[\[Mu], z] + b BesselY[\[Mu], z]) (Subscript[a, 1] BesselJ[\[Nu], z] + Subscript[b, 1] BesselY[\[Nu], z]), z] == 2^(-\[Mu] - \[Nu]) z^(\[Alpha] - \[Mu] - \[Nu]) ((1/Gamma[1 - \[Nu]]) (4^\[Nu] Csc[Pi \[Nu]] (-((4^\[Mu] b Csc[Pi \[Mu]] HypergeometricPFQ[{1/2 - \[Mu]/2 - \[Nu]/2, 1 - \[Mu]/2 - \[Nu]/2, \[Alpha]/2 - \[Mu]/2 - \[Nu]/2}, {1 - \[Mu], 1 - \[Nu], 1 - \[Mu] - \[Nu], 1 + \[Alpha]/2 - \[Mu]/2 - \[Nu]/2}, -z^2])/((-\[Alpha] + \[Mu] + \[Nu]) Gamma[1 - \[Mu]])) - (z^(2 \[Mu]) (a + b Cot[Pi \[Mu]]) HypergeometricPFQ[{1/2 + \[Mu]/2 - \[Nu]/2, 1 + \[Mu]/2 - \[Nu]/2, \[Alpha]/2 + \[Mu]/2 - \[Nu]/2}, {1 + \[Mu], 1 - \[Nu], 1 + \[Mu] - \[Nu], 1 + \[Alpha]/2 + \[Mu]/2 - \[Nu]/2}, -z^2])/ ((\[Alpha] + \[Mu] - \[Nu]) Gamma[1 + \[Mu]])) Subscript[b, 1]) - (4^\[Mu] b z^(2 \[Nu]) Csc[Pi \[Mu]] HypergeometricPFQ[ {1/2 - \[Mu]/2 + \[Nu]/2, 1 - \[Mu]/2 + \[Nu]/2, \[Alpha]/2 - \[Mu]/2 + \[Nu]/2}, {1 - \[Mu], 1 + \[Alpha]/2 - \[Mu]/2 + \[Nu]/2, 1 + \[Nu], 1 - \[Mu] + \[Nu]}, -z^2] (Subscript[a, 1] + Cot[Pi \[Nu]] Subscript[b, 1]))/ ((\[Alpha] - \[Mu] + \[Nu]) Gamma[1 - \[Mu]] Gamma[1 + \[Nu]]) + (z^(2 (\[Mu] + \[Nu])) (a + b Cot[Pi \[Mu]]) HypergeometricPFQ[ {1/2 + \[Mu]/2 + \[Nu]/2, 1 + \[Mu]/2 + \[Nu]/2, \[Alpha]/2 + \[Mu]/2 + \[Nu]/2}, {1 + \[Mu], 1 + \[Alpha]/2 + \[Mu]/2 + \[Nu]/2, 1 + \[Nu], 1 + \[Mu] + \[Nu]}, -z^2] (Subscript[a, 1] + Cot[Pi \[Nu]] Subscript[b, 1]))/ ((\[Alpha] + \[Mu] + \[Nu]) Gamma[1 + \[Mu]] Gamma[1 + \[Nu]]))










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