Chebyshev series approximations for the bessel function Y_n(z) of complex argument

We employ the truncated Chebyshev series to approximate the Bessel function of the second kind Y_n( z) for |z| ≤ 8. Detailed manipulations and discussions for Y₀( z) and Y₁( z) are given. Results of numerical experiments 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.