KelvinBei[z] \[Proportional] (-((-1)^(3/4)/(2 Sqrt[2 Pi]))) (E^(z/Sqrt[2]) (E^((I z)/Sqrt[2])/Sqrt[(-1)^(3/4) z] - 1/(E^((I z)/Sqrt[2]) Sqrt[(-1)^(1/4) z])) + (-(E^((I z)/Sqrt[2])/Sqrt[(-(-1)^(1/4)) z]) + 1/(E^((I z)/Sqrt[2]) Sqrt[(-(-1)^(3/4)) z]))/E^(z/Sqrt[2]) - ((-1)^(3/4)/(8 z)) (E^(z/Sqrt[2]) (E^((I z)/Sqrt[2])/Sqrt[(-1)^(3/4) z] - I/(E^((I z)/Sqrt[2]) Sqrt[(-1)^(1/4) z])) + ((I E^((I z)/Sqrt[2]))/Sqrt[(-(-1)^(1/4)) z] - 1/(E^((I z)/Sqrt[2]) Sqrt[(-(-1)^(3/4)) z]))/E^(z/Sqrt[2])) - ((9 I)/(128 z^2)) (E^(z/Sqrt[2]) (E^((I z)/Sqrt[2])/Sqrt[(-1)^(3/4) z] + 1/(E^((I z)/Sqrt[2]) Sqrt[(-1)^(1/4) z])) + (E^((I z)/Sqrt[2])/Sqrt[(-(-1)^(1/4)) z] + 1/(E^((I z)/Sqrt[2]) Sqrt[(-(-1)^(3/4)) z]))/E^(z/Sqrt[2])) + ((75 (-1)^(1/4))/(1024 z^3)) ((-E^(z/Sqrt[2])) (E^((I z)/Sqrt[2])/Sqrt[(-1)^(3/4) z] + I/(E^((I z)/Sqrt[2]) Sqrt[(-1)^(1/4) z])) + ((I E^((I z)/Sqrt[2]))/Sqrt[(-(-1)^(1/4)) z] + 1/(E^((I z)/Sqrt[2]) Sqrt[(-(-1)^(3/4)) z]))/E^(z/Sqrt[2])) + \[Ellipsis]) /; (Abs[z] -> Infinity)

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2007-05-02