Tau-method approximations for the Bessel function \(Y_ 0 (z)\) (Q1900539)

Let \(Y_0(z)\) be the Bessel function of the second type and order zero. The paper is devoted to the computation of \(Y_0 (z)\) by means of polynomial approximation in circular sectors. The authors apply the direct and integrated \(\tau\)-method using Faber polynomials as perturbation term to modify the Bessel differential equation. Numerical experiments related to the approximation of \(Y_0(z)\) for \(|z|\leq 8\) with six and two sectors covering the first quadrant of the complex plane, are reported in tables containing maximum and minimum absolute errors in different sectors.