Volterra-type convolution of classical polynomials

2018/04/26 by Loureiro, Ana F., Xu, Kuan
#33C05 #33C20 #33C45 #41A10 #41A58 #42A10 #42A85 #44A35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1804.10144

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 °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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