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BesselY






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.03.06.0008.01









  


  










Input Form





BesselY[\[Nu], z] \[Proportional] (1/Sqrt[z]) Sqrt[2/Pi] (Sin[z - (Pi/4) (1 + 2 \[Nu])] HypergeometricPFQ[ {1/4 - \[Nu]/2, 3/4 - \[Nu]/2, 1/4 + \[Nu]/2, 3/4 + \[Nu]/2}, {1/2}, -(1/z^2)] + ((4 \[Nu]^2 - 1)/(8 z)) Cos[z - (Pi/4) (1 + 2 \[Nu])] HypergeometricPFQ[{3/4 - \[Nu]/2, 5/4 - \[Nu]/2, 3/4 + \[Nu]/2, 5/4 + \[Nu]/2}, {3/2}, -(1/z^2)]) /; Abs[Arg[z]] < 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)





2001-10-29