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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 powers of the direct function and a power function > Linear arguments





http://functions.wolfram.com/03.03.21.0054.01









  


  








Input Form





Integrate[z^(1 - 2 \[Nu]) BesselY[\[Nu], a z]^2, z] == (1/(a^2 (-1 + 2 \[Nu]) Gamma[\[Nu]]^2)) ((2^(-1 - 2 \[Nu]) (4 (a z)^(2 \[Nu]) Cot[Pi \[Nu]]^2 - 4^\[Nu] a^2 z^2 BesselJ[-1 + \[Nu], a z]^2 Cot[Pi \[Nu]]^2 Gamma[\[Nu]]^2 - 4^\[Nu] a^2 z^2 BesselJ[\[Nu], a z]^2 Cot[Pi \[Nu]]^2 Gamma[\[Nu]]^2 - 4^\[Nu] a^2 z^2 BesselJ[-2 + \[Nu], a z] BesselJ[-\[Nu], a z] Cot[Pi \[Nu]] Csc[Pi \[Nu]] Gamma[\[Nu]]^2 - 2^(1 + 2 \[Nu]) a z BesselJ[-1 + \[Nu], a z] (a z BesselJ[1 - \[Nu], a z] - (-1 + \[Nu]) BesselJ[-\[Nu], a z]) Cot[Pi \[Nu]] Csc[Pi \[Nu]] Gamma[\[Nu]]^2 - a z (2^(1 + 2 \[Nu]) (-1 + \[Nu]) BesselJ[1 - \[Nu], a z] + 4^\[Nu] a z BesselJ[2 - \[Nu], a z]) BesselJ[\[Nu], a z] Cot[Pi \[Nu]] Csc[Pi \[Nu]] Gamma[\[Nu]]^2 - 4^\[Nu] a^2 z^2 BesselJ[1 - \[Nu], a z]^2 Csc[Pi \[Nu]]^2 Gamma[\[Nu]]^2 - 4^\[Nu] a^2 z^2 BesselJ[-\[Nu], a z]^2 Csc[Pi \[Nu]]^2 Gamma[\[Nu]]^2))/ z^(2 \[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