Volterra-type convolution of classical polynomials

Loureiro, Ana F.; Xu, Kuan

doi:10.1090/mcom/3427

Volterra-type convolution of classical polynomials
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by Ana F. Loureiro and Kuan Xu HTML | PDF

Math. Comp. 88 (2019), 2351-2381 Request permission

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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