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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Series representations > Asymptotic series expansions > Expansions for any z in trigonometric form > Using trigonometric functions with branch cut-containing arguments





http://functions.wolfram.com/03.03.06.0013.01









  


  










Input Form





BesselY[\[Nu], z] \[Proportional] (Sqrt[2/Pi] Csc[Pi \[Nu]] ((z^(2 \[Nu]) Cos[Pi \[Nu]] Cos[Sqrt[z^2] - ((1 + 2 \[Nu])/4) Pi] - (z^2)^\[Nu] Cos[Sqrt[z^2] - ((1 - 2 \[Nu])/4) Pi]) (1 + O[1/z^2]) - ((4 \[Nu]^2 - 1)/(8 Sqrt[z^2])) (z^(2 \[Nu]) Cos[Pi \[Nu]] Sin[Sqrt[z^2] - ((1 + 2 \[Nu])/4) Pi] - (z^2)^\[Nu] Sin[Sqrt[z^2] - ((1 - 2 \[Nu])/4) Pi]) (1 + O[1/z^2])))/ (z^\[Nu] (z^2)^((1 + 2 \[Nu])/4)) /; (Abs[z] -> Infinity) && !Element[\[Nu], Integers]










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





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