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variants of this functions
KelvinKer




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.16.06.0035.01









  


  








Input Form





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