Chebyshev series approximations for the Bessel function Yn(z) of complex argument

摘要

We employ the truncated Chebyshev series to approximate the Bessel function of the second kind Yn(z) for |z| ≤ 8. Detailed manipulations and discussions for Y0(z) and Y1(z) are given. Results of numerical experiments are presents are presented to demonstrate the computed accuracy by using the Chebyshev series approximations. Advantages and disadvantages of the Chebyshev series approximation compared with other polynomial approximation methods, e.g., the tau-method approximations, are discussed.