d-Orthogonality via generating functions
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摘要
In this paper, starting from a suitable generating function of a polynomial set, we show how to decide whether the considered polynomial set is d-orthogonal and, if it is so, how to determine the corresponding d-dimensional functional vector. Then, we apply the obtained results to some known and new d-orthogonal polynomial sets. For the known ones, we give new proofs for some already obtained results.
论文关键词：d-orthogonal polynomials,Linear functionals,Generating functions,Lowering operators,Transform operator,Integral representations,Sheffer polynomials,Brenke polynomials,Hypergeometric polynomials
论文评审过程：Received 30 August 2004, Revised 28 January 2005, Available online 18 January 2006.
论文官网地址：https://doi.org/10.1016/j.cam.2005.01.051
