Modified Bessel function of the first kind: Integration (formula 03.02.21.0085)

BesselI

$Mathematica Notation$

Bessel-Type Functions

BesselI[nu,z]

Integration

Indefinite integration

Involving direct function and Bessel-type functions

Involving Bessel functions

Involving Bessel J and power

Power arguments

http://functions.wolfram.com/03.02.21.0085.01

Input Form

Integrate[z^(\[Alpha] - 1) BesselJ[\[Nu], a z^r] BesselI[\[Nu], a z^r], z] == (1/r) (2^(-2 - 3 \[Nu]) Sqrt[Pi] z^\[Alpha] (a z^r)^(2 \[Nu]) Gamma[(\[Alpha] + 2 r \[Nu])/(4 r)] HypergeometricPFQRegularized[ {(\[Alpha] + 2 r \[Nu])/(4 r)}, {1 + \[Nu], (1 + \[Nu])/2, (2 + \[Nu])/2, (1/4) (4 + \[Alpha]/r + 2 \[Nu])}, (-(1/64)) a^4 z^(4 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