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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 trigonometric form > Using trigonometric functions with branch cut-free arguments





http://functions.wolfram.com/03.01.06.0013.01









  


  










Input Form





BesselJ[\[Nu], z] \[Proportional] (1/Sqrt[2 Pi]) ((1/Sqrt[z]) (1 - (I Sqrt[-z^2])/z) Cos[z - (Pi (2 \[Nu] + 1))/4] + (E^(I Pi \[Nu])/Sqrt[-z]) (1 + (I Sqrt[-z^2])/z) Cos[z + (Pi (2 \[Nu] + 1))/4]) (1 + O[1/z^2]) + ((1 - 4 \[Nu]^2)/(8 z Sqrt[2 Pi])) ((1/Sqrt[z]) (1 - (I Sqrt[-z^2])/z) Sin[z - (Pi (2 \[Nu] + 1))/4] + (E^(I Pi \[Nu])/Sqrt[-z]) (1 + (I Sqrt[-z^2])/z) Sin[z + (Pi (2 \[Nu] + 1))/4]) (1 + O[1/z^2]) /; (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)





2001-10-29