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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-free arguments





http://functions.wolfram.com/03.03.06.0015.02









  


  










Input Form





BesselY[\[Nu], z] \[Proportional] (Csc[Pi \[Nu]]/Sqrt[2 Pi]) (((z + I Sqrt[-z^2]) Cos[z + (1/4) Pi (1 - 2 \[Nu])])/ (E^(I Pi \[Nu]) (-z)^(3/2)) - ((z - I Sqrt[-z^2]) Cos[z + (1/4) Pi (-1 + 2 \[Nu])])/z^(3/2) + Cos[Pi \[Nu]] (((z - I Sqrt[-z^2]) Cos[z - (1/4) Pi (1 + 2 \[Nu])])/ z^(3/2) + (E^(I Pi \[Nu]) z (z + I Sqrt[-z^2]) Cos[z + (1/4) Pi (1 + 2 \[Nu])])/(-z)^(5/2))) (1 + O[1/z]) /; (Abs[z] -> Infinity) && !Element[\[Nu], Integers]










Standard Form





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MathML Form







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</ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <cos /> <apply> <times /> <pi /> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <pi /> <ci> &#957; </ci> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <cos /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <pi /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; 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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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