Some discrete d-orthogonal polynomial sets

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摘要

In this paper, we characterize all polynomial sets which are at the same time d-orthogonal and Δω-Appell. The resulting polynomials reduce to Charlier polynomials for (d,ω)=(1,1). Various properties of the obtained polynomials are singled out: generating function, recurrence relation of order d+1 and a difference equation of order d+1. We also explicitly express the d-dimensional functional for which the d-orthogonality holds.

论文关键词:33C45,42C05,Orthogonal polynomials,Multiple orthogonal polynomials,d-orthogonal polynomials,Difference operators,d-dimensional functionals

论文评审过程:Received 14 April 2002, Available online 6 May 2003.

论文官网地址:https://doi.org/10.1016/S0377-0427(02)00914-7