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SphericalBesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > SphericalBesselJ[nu,z] > Specific values > Specialized values > For fixed z > Symbolic rational nu





http://functions.wolfram.com/03.21.03.0038.01









  


  










Input Form





SphericalBesselJ[\[Nu], z] == ((I^((-(2/3) + Abs[1/2 + \[Nu]]) (1 + Sign[1/2 + \[Nu]])) 2^(-(17/6) + Abs[1/2 + \[Nu]]) Sqrt[Pi] z^(-(1/2) - Abs[1/2 + \[Nu]]) Gamma[-(2/3)] Sign[1/2 + \[Nu]])/(3 3^(5/6) Gamma[1 - Abs[1/2 + \[Nu]]])) (-4 2^(1/3) 3^(1/6) (3 AiryAiPrime[(-(3/2)^(2/3)) z^(2/3)] + Sqrt[3] AiryBiPrime[(-(3/2)^(2/3)) z^(2/3)] Sign[1/2 + \[Nu]]) Sum[((z^2)^k (-(2/3) - k + Abs[1/2 + \[Nu]])!)/ (4^k (k! (-(2/3) - 2 k + Abs[1/2 + \[Nu]])! Pochhammer[2/3, k] Pochhammer[1 - Abs[1/2 + \[Nu]], k])), {k, 0, -(2/3) + Abs[1/2 + \[Nu]]}] + 9 z^(4/3) (Sqrt[3] AiryAi[(-(3/2)^(2/3)) z^(2/3)] + AiryBi[(-(3/2)^(2/3)) z^(2/3)] Sign[1/2 + \[Nu]]) Sum[((z^2)^k (-(5/3) - k + Abs[1/2 + \[Nu]])!)/ (4^k (k! (-(5/3) - 2 k + Abs[1/2 + \[Nu]])! Pochhammer[5/3, k] Pochhammer[1 - Abs[1/2 + \[Nu]], k])), {k, 0, -(5/3) + Abs[1/2 + \[Nu]]}]) /; Element[Abs[1/2 + \[Nu]] - 2/3, Integers]










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