On polynomial transformations preserving purely imaginary zeros

Hindmarsh, J. L. and Lettington, M. C. ORCID: https://orcid.org/0000-0001-9327-143X 2023. On polynomial transformations preserving purely imaginary zeros. Integral Transforms and Special Functions 34 (7) , pp. 522-536. 10.1080/10652469.2022.2155643

Preview

PDF - Accepted Post-Print Version Available under License Creative Commons Attribution Non-commercial. Download (140kB) | Preview

Abstract

In this present work polynomial transformations are identified that preserve the property of the polynomials having all zeros lying on the imaginary axis. Existence results concerning families of polynomials whose generalized Mellin transforms have zeros all lying on the critical line Rs=12 are then derived. Inherent structures are identified from which a simple proof relating to the Gegenbauer family of orthogonal polynomials is subsequently deduced. Some discussion about the choice of generalized Mellin transform is also given.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Taylor & Francis
ISSN:	1065-2469
Date of First Compliant Deposit:	5 December 2022
Date of Acceptance:	3 December 2022
Last Modified:	13 Nov 2024 03:30
URI:	https://orca.cardiff.ac.uk/id/eprint/154674

Actions (repository staff only)

Edit Item