Spherical Bessel function of the first kind: Series representations (formula 03.21.06.0058)

SphericalBesselJ

$Mathematica Notation$

Bessel-Type Functions

SphericalBesselJ[nu,z]

Series representations

Asymptotic series expansions

Expansions for any z in exponential form

Using exponential function with branch cut-containing arguments

http://functions.wolfram.com/03.21.06.0058.01

Input Form

SphericalBesselJ[\[Nu], z] \[Proportional] (I/2) z^\[Nu] (z^2)^((1/2) (-1 - \[Nu])) (E^((-I) Sqrt[z^2] + (I Pi \[Nu])/2) HypergeometricPFQ[ {-\[Nu], 1 + \[Nu]}, {}, I/(2 Sqrt[z^2])] - E^(I Sqrt[z^2] - (I Pi \[Nu])/2) HypergeometricPFQ[{-\[Nu], 1 + \[Nu]}, {}, -(I/(2 Sqrt[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