Towards the Centenary of Sheffer Polynomial Sequences: Old and Recent Results

Francesco Aldo Costabile, Maria Italia Gualtieri () and Anna Napoli
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Francesco Aldo Costabile: Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy
Maria Italia Gualtieri: Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy
Anna Napoli: Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy

Mathematics, 2022, vol. 10, issue 23, 1-28

Abstract: Sheffer’s work is about to turn 100 years after its publication. In reporting this important event, we recall some interesting old and recent results, aware of the incompleteness of the wide existing literature. Particularly, we recall Sheffer’s approach, the theory of Rota and his collaborators, the isomorphism between the group of Sheffer polynomial sequences and the so-called Riordan matrices group. This inspired the most recent approaches based on elementary matrix calculus. The interesting problem of orthogonality in the context of Sheffer sequences is also reported, recalling the results of Sheffer, Meixner, Shohat, and the very recent one of Galiffa et al., and of Costabile et al.

Keywords: sheffer sequence; recurrence relation; polynomial sequences; generating functions; umbral calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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