Spherical Bessel function of the first kind: Integration (formula 03.21.21.0029)

SphericalBesselJ

$Mathematica Notation$

Bessel-Type Functions

SphericalBesselJ[nu,z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving cos

Power arguments

http://functions.wolfram.com/03.21.21.0029.01

Input Form

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

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