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BesselJ






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.01.06.0064.01









  


  










Input Form





BesselJ[\[Nu], z] \[Proportional] ((-1)^\[Nu]/Sqrt[-2 Pi z]) (HypergeometricPFQ[{1/2 + \[Nu], 1/2 - \[Nu]}, {}, I/(2 z)]/ E^(I (((2 \[Nu] + 1)/4) Pi + z)) + E^(I (((2 \[Nu] + 1)/4) Pi + z)) HypergeometricPFQ[{1/2 + \[Nu], 1/2 - \[Nu]}, {}, -(I/(2 z))]) /; 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