Abstract
This paper is to complete and improve the work reported in [1,2], using the Lanczos τ-method (in Coleman's version) to approximate the Bessel functions Y 0 ( z ) and Y 1 ( 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 τ-method. Numerical comparison among the power series, the Chebyshev series and the τ-method are conducted to show the accuracy improvement achieved by this new version of the τ-method. Some concluding remarks and suggestions on future research are given.
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