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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/03.03.21.0060.01









  


  








Input Form





Integrate[BesselY[\[Nu], a z]^2/z^2, z] == (1/(z (-1 + 4 \[Nu]^2))) (2 a^2 z^2 BesselJ[-1 + \[Nu], a z]^2 Cot[Pi \[Nu]]^2 + 2 a z BesselJ[-1 + \[Nu], a z] (2 a z BesselJ[1 - \[Nu], a z] + BesselJ[-\[Nu], a z] - BesselJ[\[Nu], a z] Cos[Pi \[Nu]]) Cot[Pi \[Nu]] Csc[Pi \[Nu]] + (1/2) Csc[Pi \[Nu]] (4 a^2 z^2 BesselJ[-2 + \[Nu], a z] (BesselJ[-\[Nu], a z] - BesselJ[\[Nu], a z] Cos[Pi \[Nu]]) Cot[Pi \[Nu]] + (4 a^2 z^2 BesselJ[-1 - \[Nu], a z]^2 - 4 a^2 z^2 BesselJ[-2 - \[Nu], a z] BesselJ[-\[Nu], a z] - 4 a z BesselJ[-1 - \[Nu], a z] BesselJ[-\[Nu], a z] + 2 BesselJ[-\[Nu], a z]^2 + 4 \[Nu] BesselJ[-\[Nu], a z]^2 + BesselJ[\[Nu], a z]^2 - 2 \[Nu] BesselJ[\[Nu], a z]^2 - 4 a z BesselJ[1 - \[Nu], a z] BesselJ[\[Nu], a z] Cos[Pi \[Nu]] + 4 a^2 z^2 BesselJ[2 - \[Nu], a z] BesselJ[\[Nu], a z] Cos[Pi \[Nu]] - 4 BesselJ[-\[Nu], a z] BesselJ[\[Nu], a z] Cos[Pi \[Nu]] + 8 \[Nu] BesselJ[-\[Nu], a z] BesselJ[\[Nu], a z] Cos[Pi \[Nu]] + BesselJ[\[Nu], a z]^2 Cos[2 Pi \[Nu]] - 2 \[Nu] BesselJ[\[Nu], a z]^2 Cos[2 Pi \[Nu]]) Csc[Pi \[Nu]]))








Standard Form





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MathML Form







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</mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> J </mi> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> J </mi> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> J </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msup> <mrow> <msub> <mi> J </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> J </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; 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Rule Form





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





2001-10-29