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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/03.03.21.0096.01









  


  








Input Form





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