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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 exponential form > Using exponential function with branch cut-containing arguments





http://functions.wolfram.com/03.03.06.0010.01









  


  










Input Form





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





© 1998- Wolfram Research, Inc.