Hyperasymptotic expansions of the modified Bessel function of the third kind of purely imaginary order

In this paper, we use a new method to derive hyperasymptotic expansions for the modified Bessel function of the third kind of purely imaginary order. Our approach is based on the method of Hadamard-series expansion developed by Paris (Proc. Roy. Soc. Lond. A 457 (2001), 2855–2869). Modifications are made to deal with the presence of an infinite number of saddle points, and numerical computation is used to illustrate the accuracy of our results.