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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/03.03.21.0070.01









  


  








Input Form





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








Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> &#945; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> </mfrac> <mo> - </mo> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mn> 2 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> </mrow> <mo> , </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> , </mo> <mrow> <mfrac> <mi> &#945; </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> </mfrac> <mo> - </mo> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;3&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[&quot;3&quot;, &quot;2&quot;], &quot;-&quot;, &quot;\[Nu]&quot;]], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;\[Alpha]&quot;, RowBox[List[&quot;2&quot;, &quot; 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</ci> </apply> </apply> <apply> <plus /> <ci> &#957; </ci> <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> <sin /> <apply> <times /> <pi /> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <pi /> <apply> <plus /> <ci> r </ci> <ci> &#945; </ci> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <ci> &#957; </ci> <apply> <ci> BesselJ </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> <apply> <ci> BesselJ </ci> <ci> &#957; </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29