A Note on the Tau-Method Approximations for Bessel Functions Y0(z) and Y1(z)

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


This paper is to complete and improve the work reported in earlier papers Tau-method approximations for the Bessel function Y0(z) and Tau-method approximations for the Bessel function Y1(z) . These methods use the Lanczos tau-method (in Coleman's version) to approximate the Bessel functions Y0(z) and Y1(z). We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the tau-method. Numerical comparison among the power series, the Chebyshev series and the tau-method are conducted to show the accuracy improvement achieved by this new version of the tau-method. Some concluding remarks and suggestions on future research are given.

Key words and phrases: Tau-method approximation, Bessel function.

This article has been published in Computers and Mathematics with Applications, Vol. 31, No. 9, pp. 63-70 (1996).