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BesselY






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.03.21.0071.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) BesselY[-\[Nu], a z^r] BesselY[\[Nu], a z^r], z] == (1/2) z^\[Alpha] Csc[Pi \[Nu]] (-((1/(Pi \[Alpha] \[Nu])) ((3 + Cos[2 Pi \[Nu]]) HypergeometricPFQ[{1/2, \[Alpha]/(2 r)}, {1 + \[Alpha]/(2 r), 1 - \[Nu], 1 + \[Nu]}, (-a^2) z^(2 r)])) + (2^(1 - 2 \[Nu]) Cot[Pi \[Nu]] ((16^\[Nu] HypergeometricPFQ[{1/2 - \[Nu], \[Alpha]/(2 r) - \[Nu]}, {1 - 2 \[Nu], 1 - \[Nu], 1 + \[Alpha]/(2 r) - \[Nu]}, (-a^2) z^(2 r)])/((\[Alpha] - 2 r \[Nu]) Gamma[1 - \[Nu]]^2) + ((a z^r)^(4 \[Nu]) HypergeometricPFQ[{1/2 + \[Nu], \[Alpha]/(2 r) + \[Nu]}, {1 + \[Nu], 1 + \[Alpha]/(2 r) + \[Nu], 1 + 2 \[Nu]}, (-a^2) z^(2 r)])/((\[Alpha] + 2 r \[Nu]) Gamma[1 + \[Nu]]^2)))/(a z^r)^(2 \[Nu]))










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <cot /> <apply> <times /> <pi /> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> &#945; </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#957; </ci> </apply> </list> <list> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 16 </cn> <ci> &#957; </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> &#945; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> <ci> &#957; 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29