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

作者：Nemes Gergo^*

来源：Analysis and Applications, 2014, 12(4): 403-462.

DOI：10.1142/S021953051450033X

• Asymptotic expansions
• Hankel functions
• Bessel functions
• error bounds
• Stokes phenomenon
• resurgence
• late coefficients

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 Berry and Howls [Hyperasymptotics for integrals with saddles, 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 numerically computable error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities.

• 出版日期2014-7