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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/03.03.21.0102.01









  


  










Input Form





Integrate[(1/z) ((a BesselJ[\[Nu], a z] + b BesselY[\[Nu], a z]) (Subscript[a, 1] BesselJ[\[Nu], a z] + Subscript[b, 1] BesselY[\[Nu], a z])), z] == (4^(-1 - \[Nu]) (2 (a z)^(4 \[Nu]) (a + b Cot[Pi \[Nu]]) Gamma[1 - \[Nu]]^2 HypergeometricPFQ[{\[Nu], 1/2 + \[Nu]}, {1 + \[Nu], 1 + \[Nu], 1 + 2 \[Nu]}, (-a^2) z^2] (Subscript[a, 1] + Cot[Pi \[Nu]] Subscript[b, 1]) + 4^\[Nu] Csc[Pi \[Nu]]^2 Gamma[1 + \[Nu]] (-4 b (a z)^(2 \[Nu]) \[Nu] Gamma[1 - \[Nu]] Log[z] Sin[Pi \[Nu]] Subscript[a, 1] - (2^(1 + 2 \[Nu]) b Gamma[1 + \[Nu]] HypergeometricPFQ[ {1/2 - \[Nu], -\[Nu]}, {1 - 2 \[Nu], 1 - \[Nu], 1 - \[Nu]}, (-a^2) z^2] - (a z)^(2 \[Nu]) \[Nu] Gamma[1 - \[Nu]] (a^2 b z^2 Cos[Pi \[Nu]] Gamma[1 - \[Nu]] Gamma[1 + \[Nu]] HypergeometricPFQRegularized[{1, 1, 3/2}, {2 - \[Nu], 2 + \[Nu], 2, 2}, (-a^2) z^2] - 4 Log[z] (2 b Cos[Pi \[Nu]] + a Sin[Pi \[Nu]]))) Subscript[b, 1] + (a z)^(2 (1 + \[Nu])) \[Nu] Gamma[1 - \[Nu]]^2 Gamma[1 + \[Nu]] HypergeometricPFQRegularized[ {1, 1, 3/2}, {2 + \[Nu], 2 - \[Nu], 2, 2}, (-a^2) z^2] (b Sin[Pi \[Nu]] Subscript[a, 1] + (b Cos[Pi \[Nu]] + a Sin[Pi \[Nu]]) Subscript[b, 1]))))/(a z)^(2 \[Nu])/ (\[Nu] Gamma[1 - \[Nu]]^2 Gamma[1 + \[Nu]]^2)










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