Bessel function of the second kind: Integration (formula 03.03.21.0077)

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

Power arguments

http://functions.wolfram.com/03.03.21.0077.01

Input Form

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