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variants of this functions
KelvinBei




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinBei[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/03.13.06.0039.01









  


  








Input Form





KelvinBei[z] \[Proportional] Piecewise[{{((-1)^(1/8) (-(-1)^(3/4) - (-1)^(1/4) E^(2 (-1)^(1/4) z) - E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Inequality[-(1/4), Less, Arg[z]/Pi, LessEqual, 1/4]}, {((-1)^(1/8) (-(-1)^(3/4) + (-1)^(1/4) E^(2 (-1)^(1/4) z) - E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Inequality[1/4, Less, Arg[z]/Pi, LessEqual, 3/4]}, {((-1)^(1/8) (-(-1)^(3/4) + (-1)^(1/4) E^(2 (-1)^(1/4) z) - E^(I Sqrt[2] z) - I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Arg[z]/Pi > 3/4}, {((-1)^(1/8) (-(-1)^(3/4) - (-1)^(1/4) E^(2 (-1)^(1/4) z) + E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Inequality[-(3/4), Less, Arg[z]/Pi, LessEqual, -(1/4)]}}, ((-1)^(1/8) ((-1)^(3/4) - (-1)^(1/4) E^(2 (-1)^(1/4) z) + E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z]))] /; (Abs[z] -> Infinity)








Standard Form





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MathML Form







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





2007-05-02