Volterra-type convolution of classical polynomials

Loureiro, Ana F., Xu, Kuan (2019) Volterra-type convolution of classical polynomials. Mathematics of Computation, 88 . pp. 2351-2381. ISSN 0025-5718. E-ISSN 1088-6842. (doi:10.1090/mcom/3427) (KAR id:66954)

PDF Author's Accepted Manuscript Language: English This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Download this file (PDF/745kB)	Preview
Request a format suitable for use with assistive technology e.g. a screenreader
Official URL: https://doi.org/10.1090/mcom/3427
Additional URLs: https://arxiv.org/abs/1804.10144 Publisher

Abstract

We present a general framework for calculating the Volterra-type convolution of polynomials from an arbitrary polynomial sequence {Pk(x)}k?0 with degPk(x)=k. Based on this framework, series representations for the convolutions of classical orthogonal polynomials, including Jacobi and Laguerre families, are derived, along with some relevant results pertaining to these new formulas.

Item Type:	Article
DOI/Identification number:	10.1090/mcom/3427
Uncontrolled keywords:	convolution, Volterra convolution integral, orthogonal polynomials, Jacobi polynomials, Gegenbauer polynomials, Legendre polynomials, Chebyshev polynomials, Laguerre polynomials
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA351 Special functions
Institutional Unit:	Schools > School of Engineering, Mathematics and Physics > Mathematical Sciences
Former Institutional Unit:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Ana F. Loureiro
Date Deposited:	08 May 2018 21:07 UTC
Last Modified:	20 May 2025 11:39 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/66954 (The current URI for this page, for reference purposes)

University of Kent Author Information

Loureiro, Ana F..

Creator's ORCID:	https://orcid.org/0000-0002-4137-8822
CReDIT Contributor Roles:

Xu, Kuan.

Creator's ORCID:
CReDIT Contributor Roles:

Depositors only (login required):

Altmetric

Total Views

Total unique views of this page since July 2020. For more details click on the image.