Open AccessComputation of the reverse generalized Bessel polynomials and their zeros
Author(s) -
Dunster T. Mark,
Gil Amparo,
RuizAntolín Diego,
Segura Javier
Publication year - 2021
Publication title -
computational and mathematical methods
Language(s) - English
Resource type - Journals
ISSN - 2577-7408
DOI - 10.1002/cmm4.1198
Subject(s) - bessel function , bessel polynomials , mathematics , computation , bessel filter , bessel process , orthogonal polynomials , filter (signal processing) , classical orthogonal polynomials , discrete orthogonal polynomials , algorithm , gegenbauer polynomials , pure mathematics , mathematical analysis , computer science , computer vision
It is well known that one of the most relevant applications of the reverse Bessel polynomialsθ n ( z ) is filter design. In particular, the poles of the transfer function of a Bessel filter are basically the zeros ofθ n ( z ) . In this article we discuss an algorithm to compute the zeros of reverse generalized Bessel polynomialsθ n ( 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.