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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself





http://functions.wolfram.com/03.03.06.0030.01









  


  










Input Form





BesselY[\[Nu], z] == (Sqrt[Pi] Csc[Pi \[Nu]] Sum[(2^k/(x^k k!)) (((-16^\[Nu]) Gamma[1 - \[Nu]] HypergeometricPFQRegularized[{(1 - \[Nu])/2, 1 - \[Nu]/2}, {(1 - \[Nu] - k)/2, (2 - \[Nu] - k)/2, 1 - \[Nu]}, -(x^2/4)])/ E^(2 I Pi \[Nu] Floor[Arg[-x + z]/(2 Pi)]) + x^(2 \[Nu]) E^(2 I Pi \[Nu] Floor[Arg[-x + z]/(2 Pi)]) Cos[Pi \[Nu]] Gamma[\[Nu] + 1] HypergeometricPFQRegularized[{(\[Nu] + 1)/2, (\[Nu] + 2)/2}, {(1 + \[Nu] - k)/2, (2 + \[Nu] - k)/2, \[Nu] + 1}, -(x^2/4)]) (z - x)^k, {k, 0, Infinity}])/(2^(2 \[Nu]) x^\[Nu]) /; !Element[\[Nu], Integers]










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <apply> <notin /> <ci> &#957; </ci> <ci> &#8484; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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