Department of Mathematics

The George Washington University

Washington, DC 20052, USA

and

John A. Belward

Centre for Industrial & Applied Mathematics & Parallel Computing

Department of Mathematics

The University of Queensland

Queensland 4072, Australia

We employ the truncated Chebyshev series to approximate the Bessel function of the second kind Y{n}(z) for |z|>=8. Detailed manipulations and discussions for Y{0}(z) and Y_{1}(z) are given. Results of numerical experiments are presented to demonstrate the computed accuracy by using the Chebyshev series approximation. Advantages and disadvantages of the Chebyshev series approximation compared with other polynomial approximation methods, e.g., the tau-method approximations, are discussed.

Key words and phrases: Polynomial approximations, Chebyshev series approximations, Tau-method approximations, complex Bessel functions.

This paper has been published in Applied Mathematics and Computation, Vol. 88 (2-3), 1997.