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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-free arguments





http://functions.wolfram.com/03.01.06.0075.01









  


  










Input Form





BesselJ[\[Nu], z] \[Proportional] Piecewise[{{((-1)^(1/4) I^\[Nu])/(E^(I z) (Sqrt[2 Pi] Sqrt[z])) - ((-1)^(3/4) I^\[Nu] E^(I z - I Pi \[Nu]))/(Sqrt[2 Pi] Sqrt[z]), Arg[z] <= 0}}, ((-1)^(1/4) I^\[Nu])/(E^(I z) (Sqrt[2 Pi] Sqrt[z])) + ((-1)^(3/4) I^\[Nu] E^(I z + I Pi \[Nu]))/(Sqrt[2 Pi] Sqrt[z])] /; (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