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variants of this functions
KelvinKer






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.16.06.0026.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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





2007-05-02