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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)

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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
Divisions: 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: 16 Feb 2021 13:54 UTC
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