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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[z] > Series representations > Asymptotic series expansions > Expansions for any z in exponential form > Using exponential function with branch cut-free arguments





http://functions.wolfram.com/03.15.06.0023.01









  


  










Input Form





KelvinKei[z] \[Proportional] Piecewise[{{((-1)^(5/8) ((-1 + I) + Sqrt[2] E^(I Sqrt[2] z)) Sqrt[Pi])/ (4 E^((-1)^(1/4) z) Sqrt[z]), 4 Arg[z] <= Pi}, {Sqrt[Pi/2] ((-1)^(3/8)/(E^((-1)^(1/4) z) (2 Sqrt[z]))) (-1 + E^(I Sqrt[2] z) ((-1)^(1/4) - 2 I E^(Sqrt[2] z))), 4 Arg[z] <= 3 Pi}}, (((-1)^(5/8) Sqrt[Pi/2])/ (E^((-1)^(1/4) z) (2 Sqrt[z]))) ((-1)^(3/4) - 2 (-1)^(1/4) E^(2 (-1)^(1/4) z) + E^(I Sqrt[2] z) + 2 I E^(Sqrt[2] z))] /; (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





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