Spherical Bessel function of the first kind: Integration (formula 03.21.21.0057)

SphericalBesselJ

$Mathematica Notation$

Bessel-Type Functions

SphericalBesselJ[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/03.21.21.0057.01

Input Form

Integrate[z^(\[Alpha] - 1) SphericalBesselJ[\[Mu], a z^r] SphericalBesselJ[\[Nu], a z^r], z] == (2^(-2 - \[Mu] - \[Nu]) Pi z^\[Alpha] (a z^r)^(\[Mu] + \[Nu]) HypergeometricPFQ[{1 + \[Mu]/2 + \[Nu]/2, 3/2 + \[Mu]/2 + \[Nu]/2, \[Alpha]/(2 r) + \[Mu]/2 + \[Nu]/2}, {3/2 + \[Mu], 1 + \[Alpha]/(2 r) + \[Mu]/2 + \[Nu]/2, 3/2 + \[Nu], 2 + \[Mu] + \[Nu]}, (-a^2) z^(2 r)])/((\[Alpha] + r (\[Mu] + \[Nu])) Gamma[3/2 + \[Mu]] Gamma[3/2 + \[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)

2007-05-02