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arXiv · 1804.10144

Volterra-type convolution of classical polynomials

Ana F. Loureiro·Kuan Xu
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Abstract

We present a general framework for calculating the Volterra-type convolution of polynomials from an arbitrary polynomial sequence $\{P_k(x)\}_{k \geqslant 0}$ with $\deg P_k(x) = k$. 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.

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BibTeXRIS

Ana F. Loureiro, Kuan Xu. 2018-04-26. Volterra-type convolution of classical polynomials. https://arxiv.org/abs/1804.10144

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