2014/04/14 by Pascal Maroni, P. Maroni, Maroni, Pascal +3
Mathematics · #11B73 #16R60 #33C45 #Advanced Mathematical Identities #Advanced Topics in Algebra #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Primary 42C05 #Secondary 44A55 #math.CA #msc:11B73 #msc:16R60 #msc:33C45 #msc:42C05 #msc:44A55
paper · pdf · doi:10.48550/arxiv.1404.3615
22 pages
arxiv created 2014/04/14 · openalex publication_date 2014/04/14 · arxiv updated 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a study of a specific kind of lowering operator, herein called Λ, which is defined as a finite sum of lowering operators, proving that this configuration can be altered, for instance, by the use of Stirling numbers. We characterize the polynomial sequences fulfilling an Appell relation with respect to Λ, and considering a concrete cubic decomposition of a simple Appell sequence, we prove that the polynomial component sequences are Λ-Appell, with Λ defined as previously, although by a three term sum. Ultimately, we prove the non-existence of orthogonal polynomial sequences which are also Λ-Appell, when Λ is the lowering operator Λ=a0D+a1DxD+a2(Dx)2D, where a0, a1 and a2 are constants and a2 ≠ 0. The case where a2=0 and a1 ≠ 0 is also naturally recaptured.