Bessel function of the first kind: Integration (formula 03.01.21.0070)

BesselJ

$Mathematica Notation$

Bessel-Type Functions

BesselJ[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/03.01.21.0070.01

Input Form

Integrate[z^(\[Alpha] - 1) BesselJ[\[Mu], a z^r] BesselJ[\[Nu], a z^r], z] == (1/r) (2^(-1 - \[Mu] - \[Nu]) z^\[Alpha] (a z^r)^(\[Mu] + \[Nu]) Gamma[1 + \[Mu] + \[Nu]] Gamma[(\[Alpha] + r (\[Mu] + \[Nu]))/(2 r)] HypergeometricPFQRegularized[{(1/2) (1 + \[Mu] + \[Nu]), (1/2) (2 + \[Mu] + \[Nu]), (\[Alpha] + r (\[Mu] + \[Nu]))/(2 r)}, {1 + \[Mu], (\[Alpha] + r (2 + \[Mu] + \[Nu]))/(2 r), 1 + \[Nu], 1 + \[Mu] + \[Nu]}, (-a^2) z^(2 r)])

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