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which decreases for real , has the following asymptotic expansion when :
where is a constant. The function is an entire function, while its asymptotic expansion is a discontinuous function.
|||G.G. Stokes, Trans. Cambridge Philos. Soc. , 10 (1864) pp. 106–128|
|||J. Heading, "An introduction to phase-integral methods" , Methuen (1962)|
|||N.G. de Bruijn, "Asymptotic methods in analysis" , Dover, reprint (1981)|
There is a recent interest in the Stokes phenomenon in asymptotic analysis, which is initiated by M.V. Berry in [a1]. In the new interpretation of the phenomenon, an error function is introduced to describe the rapid change in the behaviour of the remainders of the asymptotic expansions as a Stokes line is crossed. A rigorous treatment of Berry's observation is given in [a2].
|[a1]||M.V. Berry, "Uniform asymptotic smoothing of Stokes' discontinuities" Proc. R. Soc. London A , 422 (1989) pp. 7–21|
|[a2]||"On Stokes's phenomenon and converging factors" R. Wong (ed.) , Proc. Int. Symp. Asymptotic and Computational Anal. (Winnipeg, Manitoba) , M. Dekker (1990)|
Stokes phenomenon. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Stokes_phenomenon&oldid=26717