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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-free arguments





http://functions.wolfram.com/03.03.06.0068.01









  


  








Input Form





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





2007-05-02