Spherical Bessel function of the first kind: Integration (formula 03.21.21.0032)

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 sin and power

Power arguments

http://functions.wolfram.com/03.21.21.0032.01

Input Form

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

2007-05-02