# Volterra-type convolution of classical polynomials

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

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## 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 10.1090/mcom/3427 convolution, Volterra convolution integral, orthogonal polynomials, Jacobi polynomials, Gegenbauer polynomials, Legendre polynomials, Chebyshev polynomials, Laguerre polynomials Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA351 Special functions Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Ana F. Loureiro 08 May 2018 21:07 UTC 28 May 2019 12:59 UTC https://kar.kent.ac.uk/id/eprint/66954 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-4137-8822