Volterra-type convolution of classical polynomials

Abstract

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

arXiv comment29 pages