Computation of the reverse generalized Bessel polynomials and their zeros

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 general...

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Bibliographic Details
Published in:Computational and mathematical methods Vol. 3; no. 6
Main Authors: Dunster, T. Mark, Gil, Amparo, Ruiz‐Antolín, Diego, Segura, Javier
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.11.2021
Subjects:
Algorithms
Approximation
Asymptotic series
computation of special functions
Filter design (mathematics)
Mathematical analysis
numerical approximations
Polynomials
reverse Bessel polynomials
Transfer functions
ISSN:2577-7408, 2577-7408
Online Access:Get full text
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Summary: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.
Bibliography:Funding information
Ministerio de Ciencia e Innovación, PGC2018‐098279‐B‐I00 (MCIU/AEI/FEDER, UE)
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SourceType-Scholarly Journals-1
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content type line 14
ISSN:2577-7408
2577-7408
DOI:10.1002/cmm4.1198