Computation of the reverse generalized Bessel polynomials and their zeros - Dunster, T. Mark; Gil, Amparo; Ruiz‐Antolín, Diego; Segura, Javier (Computational and mathematical methods, 2021)
It is well known that one of the most relevant applications of the reverse Bessel polynomials θn(z) is filter design. In particular, the poles of the transfer function of a Bessel filter are basically the zeros of θn(z). In this article we discuss an algorithm to compute the zeros of reverse generalized Bessel polynomials θn(z;a). A key ingredient in the algorithm will be a method to compute the polynomials. For this purpose, we analyze the use of recurrence relations and asymptotic expansions in terms of elementary functions to obtain accurate approximations to the polynomials. The performance of all the numerical approximations will be illustrated with examples.