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BesselY




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Integration > Indefinite integration > Involving functions of the direct function > Involving elementary functions of the direct function > Involving powers of the direct function > Power arguments





http://functions.wolfram.com/03.03.21.0047.01









  


  








Input Form





Integrate[BesselY[\[Nu], a z^r]^2, z] == -((z Csc[Pi \[Nu]] (2^(1 + 2 \[Nu]) (a z^r)^(2 \[Nu]) (-1 + 4 r^2 \[Nu]^2) Cot[Pi \[Nu]] Gamma[1 - \[Nu]] Gamma[1 + \[Nu]] HypergeometricPFQ[{1/2, 1/(2 r)}, {1 + 1/(2 r), 1 - \[Nu], 1 + \[Nu]}, (-a^2) z^(2 r)] + (16^\[Nu] + 2^(1 + 4 \[Nu]) r \[Nu]) Csc[Pi \[Nu]] Gamma[1 + \[Nu]]^2 HypergeometricPFQ[{1/2 - \[Nu], 1/(2 r) - \[Nu]}, {1 - 2 \[Nu], 1 - \[Nu], 1 + 1/(2 r) - \[Nu]}, (-a^2) z^(2 r)] - (a z^r)^(4 \[Nu]) (-1 + 2 r \[Nu]) Cos[Pi \[Nu]] Cot[Pi \[Nu]] Gamma[1 - \[Nu]]^2 HypergeometricPFQ[{1/2 + \[Nu], 1/(2 r) + \[Nu]}, {1 + \[Nu], 1 + 1/(2 r) + \[Nu], 1 + 2 \[Nu]}, (-a^2) z^(2 r)]))/ (4^\[Nu] (a z^r)^(2 \[Nu])))/((-1 + 4 r^2 \[Nu]^2) 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