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

Abstract

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.

45 pages, 5 figures, accepted for publication in "Analysis and Applications"

References in corpus (2)

• An explicit formula for the coefficients in Laplace's method
• Numerical calculation of Bessel, Hankel and Airy functions

Cited by in corpus (1)

• The resurgence properties of the Hankel and Bessel functions of nearly equal order and argument