Spherical Bessel function of the first kind: Series representations (formula 03.21.06.0066)

SphericalBesselJ

$Mathematica Notation$

Bessel-Type Functions

SphericalBesselJ[nu,z]

Series representations

Asymptotic series expansions

Expansions for any z in trigonometric form

Using trigonometric functions with branch cut-containing arguments

http://functions.wolfram.com/03.21.06.0066.01

Input Form

SphericalBesselJ[\[Nu], z] \[Proportional] z^\[Nu] (z^2)^(-(1/2) - \[Nu]/2) (Sin[Sqrt[z^2] - (Pi \[Nu])/2] HypergeometricPFQ[ {1/2 - \[Nu]/2, 1/2 + \[Nu]/2, 1 + \[Nu]/2, -(\[Nu]/2)}, {1/2}, -(1/z^2)] + ((\[Nu] (1 + \[Nu]))/(2 Sqrt[z^2])) Cos[Sqrt[z^2] - (Pi \[Nu])/2] HypergeometricPFQ[ {1/2 - \[Nu]/2, 1 - \[Nu]/2, 1 + \[Nu]/2, 3/2 + \[Nu]/2}, {3/2}, -(1/z^2)]) /; (Abs[z] -> Infinity)

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