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.

Asymptotic analysis of the modified Bessel function with respect to the parameter

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

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Asymptotic analysis of the modified Bessel function with respect to the parameter

Citations

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

References

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

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