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BesselK






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselK[nu,z] > Integration > Indefinite integration > Involving direct function and Bessel-type functions > Involving Bessel functions > Involving Bessel I and power > Power arguments





http://functions.wolfram.com/03.04.21.0100.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) BesselI[\[Mu], a z^r] BesselK[\[Nu], a z^r], z] == (1/Gamma[1 + \[Mu]]) (2^(-1 - \[Mu] - \[Nu]) Pi z^\[Alpha] (a z^r)^(\[Mu] - \[Nu]) Csc[Pi \[Nu]] ((4^\[Nu] HypergeometricPFQ[{1/2 + \[Mu]/2 - \[Nu]/2, 1 + \[Mu]/2 - \[Nu]/2, \[Alpha]/(2 r) + \[Mu]/2 - \[Nu]/2}, {1 + \[Mu], 1 - \[Nu], 1 + \[Mu] - \[Nu], 1 + \[Alpha]/(2 r) + \[Mu]/2 - \[Nu]/2}, a^2 z^(2 r)])/((\[Alpha] + r (\[Mu] - \[Nu])) Gamma[1 - \[Nu]]) - ((a z^r)^(2 \[Nu]) HypergeometricPFQ[ {1/2 + \[Mu]/2 + \[Nu]/2, 1 + \[Mu]/2 + \[Nu]/2, \[Alpha]/(2 r) + \[Mu]/2 + \[Nu]/2}, {1 + \[Mu], 1 + \[Alpha]/(2 r) + \[Mu]/2 + \[Nu]/2, 1 + \[Nu], 1 + \[Mu] + \[Nu]}, a^2 z^(2 r)])/((\[Alpha] + r (\[Mu] + \[Nu])) Gamma[1 + \[Nu]])))










Standard Form





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MathML Form







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</ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </list> <list> <apply> <plus /> <ci> &#956; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> &#945; </ci> <apply> <times /> <ci> r </ci> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <ci> &#956; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> &#945; </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#956; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </list> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </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