Chebyshev Series Approximations for the Bessel Function Y{n}(z) of Complex Argument

Jun Zhang
Department of Mathematics
The George Washington University
Washington, DC 20052, USA
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.