Bessel function of the second kind: Integration (formula 03.03.21.0097)

BesselY

$Mathematica Notation$

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/03.03.21.0097.01

Input Form

Integrate[(a BesselJ[\[Nu], z] + b BesselY[\[Nu], z])^2/z, z] == (2^(-1 - 2 \[Nu]) ((-16^\[Nu]) b^2 Pi (-1 + \[Nu]^2) Csc[Pi \[Nu]]^2 Gamma[\[Nu]]^2 HypergeometricPFQ[{1/2 - \[Nu], -\[Nu]}, {1 - 2 \[Nu], 1 - \[Nu], 1 - \[Nu]}, -z^2] + z^(2 \[Nu]) (a + b Cot[Pi \[Nu]]) Gamma[-\[Nu]]^2 (Pi z^(2 \[Nu]) (-1 + \[Nu]^2) (a + b Cot[Pi \[Nu]]) HypergeometricPFQ[{\[Nu], 1/2 + \[Nu]}, {1 + \[Nu], 1 + \[Nu], 1 + 2 \[Nu]}, -z^2] - 4^\[Nu] b \[Nu]^2 Gamma[\[Nu]]^2 (z^2 HypergeometricPFQ[{1, 1, 3/2}, {2, 2, 2 - \[Nu], 2 + \[Nu]}, -z^2] + 4 (-1 + \[Nu]^2) Log[z]))))/z^(2 \[Nu])/ (Pi (-1 + \[Nu]) \[Nu]^3 (1 + \[Nu]) Gamma[-\[Nu]]^2 Gamma[\[Nu]]^2)

Standard Form

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MathML Form

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<times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> ν </ci> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <pi /> <apply> <plus /> <ci> ν </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> ν </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> ν </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29