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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 exponential form ||| In exponential form





http://functions.wolfram.com/03.13.06.0026.01









  


  










Input Form





KelvinBei[z] \[Proportional] (-(1/(2 Sqrt[2 Pi] Sqrt[-z]))) (E^(z/Sqrt[2]) (E^((I Pi)/8 - (I z)/Sqrt[2]) - E^(-((I Pi)/8) + (I z)/Sqrt[2])) + (E^((3 I Pi)/8 - (I z)/Sqrt[2]) + E^(-((3 I Pi)/8) + (I z)/Sqrt[2]))/ E^(z/Sqrt[2]) + (1/(8 z)) (E^(z/Sqrt[2]) (E^((3 I Pi)/8 - (I z)/Sqrt[2]) - E^(-((3 I Pi)/8) + (I z)/Sqrt[2])) + (-E^((I Pi)/8 - (I z)/Sqrt[2]) - E^(-((I Pi)/8) + (I z)/Sqrt[2]))/ E^(z/Sqrt[2])) + ((9 I)/(128 z^2)) (E^(z/Sqrt[2]) (E^((I Pi)/8 - (I z)/Sqrt[2]) + E^(-((I Pi)/8) + (I z)/Sqrt[2])) + (-E^((3 I Pi)/8 - (I z)/Sqrt[2]) + E^(-((3 I Pi)/8) + (I z)/Sqrt[2]))/E^(z/Sqrt[2])) + ((75 I)/(1024 z^3)) (E^(z/Sqrt[2]) (E^((3 I Pi)/8 - (I z)/Sqrt[2]) + E^(-((3 I Pi)/8) + (I z)/Sqrt[2])) + (E^((I Pi)/8 - (I z)/Sqrt[2]) - E^(-((I Pi)/8) + (I z)/Sqrt[2]))/ E^(z/Sqrt[2])) + \[Ellipsis]) /; 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





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