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A note on the tau-method approximations for the Bessel functions Y 0 (z) and Y 1 (z). (English) Zbl 0858.65013
This paper completes and improves the previous one by the author and J. A. Belward [Comput. Math. Appl. 30, No. 7, 5-14 (1995; Zbl 0834.65004)] and the one by the author [ibid. 30, No. 7, 15-19 (1995; Zbl 0834.65005)], dealing with the application of a particular version of the Lanczos τ-methods to approximate the Bessel functions Y 0 (z) and Y 1 (z) in the complex plane. That version uses Faber polynomials up to degree 15 as the perturbation terms. The author introduces symbolic representation of the scaled Faber polynomials and the appropriately modified (automated) τ-method. Numerical comparisons, showing the accuracy improvements achieved by this new version of the τ-method, are given and discussed.
MSC:
65D20Computation of special functions, construction of tables
33C10Bessel and Airy functions, cylinder functions, 0 F 1