Tau-method approximations for the Bessel function \(Y_ 1 (z)\)
The paper deals with an application of the Lanczos \(\tau\)-method in approximating the Bessel function \(Y_1(z)\) of the second kind of order one. Polynomial approximants of \(Y_1(z)\) are obtained from the Bessel differential equation after being perturbed by adding a Faber polynomial term. Maximum and minimum errors in computing \(Y_1(z)\) are listed in a table, where Chebyshev, direct and integrated \(\tau\)-methods can be compared. The present article and a related one by the author and \textit{J. A. Belward} [ibid. 30, No. 7, 5-14 (1995; reviewed above)] -- the latter contains results on the polynomial approximation of the Bessel function \(Y_0(z)\) -- make it possible to compute function values for \(Y_n(z)\), \(n > 1\), using known recurrence relations.
scientific article; zbMATH DE number 811384