Spherical Bessel function of the first kind: Integration (formula 03.21.21.0035)

SphericalBesselJ

$Mathematica Notation$

Bessel-Type Functions

SphericalBesselJ[nu,z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions and a power function

Involving cos and power

Linear arguments

http://functions.wolfram.com/03.21.21.0035.01

Input Form

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

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