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arXiv:1309.2209 [math.CA]AbstractReferencesReviewsResources

The resurgence properties of the large order asymptotics of the Hankel and Bessel functions

Gergő Nemes

Published 2013-09-09, updated 2014-03-25Version 4

The aim of this paper is to derive new representations for the Hankel and Bessel functions, exploiting the reformulation of the method of steepest descents by M. V. Berry and C. J. Howls (Berry and Howls, Proc. R. Soc. Lond. A 434 (1991) 657--675). Using these representations, we obtain a number of properties of the large order asymptotic expansions of the Hankel and Bessel functions due to Debye, including explicit and realistic error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities.

Comments: 45 pages, 5 figures, accepted for publication in "Analysis and Applications"
Journal: Analysis and Applications, Volume 12, Issue 4, 2014, 403-462
Categories: math.CA
Subjects: 41A60, 30E15, 33C10, 34M40
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