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SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Series representations > Asymptotic series expansions > Expansions inside Stokes sectors > Expansions containing z->-infinity > In trigonometric form ||| In trigonometric form





http://functions.wolfram.com/03.21.06.0052.01









  


  










Input Form





SphericalBesselJ[\[Nu], z] \[Proportional] ((I (-1)^\[Nu] Sqrt[-z])/z^(3/2)) (Sin[z + (Pi \[Nu])/2] (1 - ((-1 + \[Nu]) \[Nu] (1 + \[Nu]) (2 + \[Nu]))/ (8 z^2) + ((-3 + \[Nu]) (-2 + \[Nu]) (-1 + \[Nu]) \[Nu] (1 + \[Nu]) (2 + \[Nu]) (3 + \[Nu]) (4 + \[Nu]))/(384 z^4) + \[Ellipsis]) + ((\[Nu] (1 + \[Nu]))/(2 z)) Cos[z + (Pi \[Nu])/2] (1 - ((-2 + \[Nu]) (-1 + \[Nu]) (2 + \[Nu]) (3 + \[Nu]))/(24 z^2) + ((-4 + \[Nu]) (-3 + \[Nu]) (-2 + \[Nu]) (-1 + \[Nu]) (2 + \[Nu]) (3 + \[Nu]) (4 + \[Nu]) (5 + \[Nu]))/(1920 z^4) + \[Ellipsis])) /; Inequality[0, Less, Arg[z], LessEqual, Pi] && (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