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variants of this functions
KelvinBei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[z] > Series representations > Asymptotic series expansions > Expansions inside Stokes sectors > Expansions containing z->-infinity > In trigonometric form ||| In trigonometric form





http://functions.wolfram.com/03.13.06.0031.01









  


  










Input Form





KelvinBei[z] \[Proportional] (-(I/(Sqrt[2 Pi] Sqrt[-z]))) ((1/(2 z)) Sum[((1/z^2)^k/(4^k (1 + 2 k)!)) Pochhammer[1/2, 1 + 2 k]^2 ((I Cos[(k Pi)/2 + (1/8) (-Pi + 4 Sqrt[2] z)])/E^(z/Sqrt[2]) + (-1)^k E^(z/Sqrt[2]) Cos[(k Pi)/2 + (1/8) (Pi + 4 Sqrt[2] z)]), {k, 0, Floor[(1/2) (-1 + n)]}] + Sum[((1/z^2)^k/(4^k (2 k)!)) Pochhammer[1/2, 2 k]^2 (E^(z/Sqrt[2]) Sin[(k Pi)/2 + (1/8) (Pi - 4 Sqrt[2] z)] - (I Sin[(k Pi)/2 + (1/8) (Pi + 4 Sqrt[2] z)])/E^(z/Sqrt[2])), {k, 0, Floor[n/2]}] + \[Ellipsis]) /; (z -> -Infinity) && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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<power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <plus /> <apply> <times /> <pi /> <ci> k </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <pi /> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </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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