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BesselJ






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselJ[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/03.01.06.0070.01









  


  










Input Form





BesselJ[\[Nu], z] \[Proportional] ((1/Sqrt[2 Pi]) z^\[Nu] ((Sum[((Pochhammer[1/2 + \[Nu], k] Pochhammer[1/2 - \[Nu], k])/k!) (-(I/(2 Sqrt[z^2])))^k, {k, 0, n}] + O[1/z^(n + 1)])/ E^(I (((2 \[Nu] + 1)/4) Pi - Sqrt[z^2])) + E^(I (((2 \[Nu] + 1)/4) Pi - Sqrt[z^2])) (Sum[((Pochhammer[1/2 + \[Nu], k] Pochhammer[1/2 - \[Nu], k])/k!) (I/(2 Sqrt[z^2]))^k, {k, 0, n}] + O[1/z^(n + 1)])))/ (z^2)^((2 \[Nu] + 1)/4) /; (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