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

Abstract

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 Y 0( z) and Y 1( 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.