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

Article type: Research Article

Authors: Shi, Wei | Wong, R.

Affiliations: Department of Mathematics, Wuhan University, Wuhan, Hubei, China | Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

Abstract: 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.

Keywords: modified Bessel function of the third kind of purely imaginary order, hyperasymptotic expansion, Hadamard series

DOI: 10.3233/ASY-2008-0930

Journal: Asymptotic Analysis, vol. 63, no. 1-2, pp. 101-123, 2009