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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Representations through more general functions > Through Meijer G > Generalized cases involving 0F~1





http://functions.wolfram.com/03.03.26.0168.01









  


  










Input Form





BesselY[\[Nu], z] Hypergeometric0F1Regularized[-n - \[Nu], -(z^2/4)] == (2^(-1 - n - \[Nu])/Sqrt[Pi]) ((-1)^n MeijerG[{{(1/2) (1 + n + \[Nu]), (1/2) (2 + n + \[Nu])}, {(1 - \[Nu])/2}}, {{1 + n + \[Nu]/2, -(\[Nu]/2)}, {1 + n + (3 \[Nu])/2, \[Nu]/2, (1 - \[Nu])/2}}, z, 1/2] + 2 z^\[Nu] Cot[\[Nu] Pi] Sum[(((-1)^(k + Floor[(1 + n)/2]) z^(2 k) Gamma[1/2 + k - n + Floor[n/2]])/(k! Gamma[k - n - \[Nu]] Gamma[1 + k + \[Nu]])) Pochhammer[1 - k + Floor[n/2], n - Floor[n/2]], {k, 0, Floor[n/2]}]) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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</ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <list> <apply> <plus /> <ci> n </ci> <apply> <times /> <cn type='integer'> 3 </cn> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> </list> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.