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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/03.03.21.0055.01









  


  










Input Form





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