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variants of this functions
KelvinBer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBer[nu,z] > Series representations > Asymptotic series expansions > Expansions inside Stokes sectors > Expansions containing z->infinity > In exponential form ||| In exponential form





http://functions.wolfram.com/03.18.06.0036.01









  


  










Input Form





KelvinBer[\[Nu], z] \[Proportional] (-(1/(2 Sqrt[2 Pi] Sqrt[z]))) ((E^((3 I Pi \[Nu])/2 - (5 Pi I)/8 - (I z)/Sqrt[2]) (1 + O[1/z^2]) - E^((I Pi \[Nu])/2 + (5 Pi I)/8 + (I z)/Sqrt[2]) (1 + O[1/z^2]))/ E^(z/Sqrt[2]) - E^(z/Sqrt[2]) (E^((I Pi \[Nu])/2 - (Pi I)/8 + (I z)/Sqrt[2]) (1 + O[1/z^2]) + E^(-((I Pi \[Nu])/2) + (Pi I)/8 - (I z)/Sqrt[2]) (1 + O[1/z^2]))) /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi] && (Abs[z] -> Infinity)










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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> <apply> <power /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <ci> O </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <plus /> <apply> <times /> <imaginaryi /> <pi /> <ci> &#957; 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Rule Form





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





2007-05-02