Differential equation and recursive formulas of Sheffer polynomial sequences
type: Item
instance of: scholarly article
title: Differential equation and recursive formulas of Sheffer polynomial sequences
zbMATH Open document ID: 1237.33008
DOI: 10.5402/2011/476462
author: Heekyung Youn
author: Yongzhi Yang
published in: ISRN Discrete Mathematics
publication date: 2012-04-03T00:00:00Z
review text: Summary: We derive a differential equation and recursive formulas of Sheffer polynomial sequences utilizing matrix algebra. These formulas provide the defining characteristics of, and the means to compute, the Sheffer polynomial sequences. The tools we use are the well-known Pascal functional and Wronskian matrices. The properties and the relationship between the two matrices simplify the complexity of the generating functions of Sheffer polynomial sequences. This work extends \textit{M. X. He} and \textit{P. E. Ricci}'s work [J. Comput. Appl. Math. 139, 231--237 (2002; Zbl 0994.33008)] to a broader class of polynomial sequences, from Appell to Sheffer, using a different method. The work is self-contained.
Mathematics Subject Classification ID: 33C65
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 6021220
zbMATH Keywords: recursive formulas of Sheffer polynomial sequences
zbMATH Keywords: Pascal functional
zbMATH Keywords: Wronskian matrices
Wikidata QID: Q58689461
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2011/476462
OpenAlex ID: W2088650450
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description: scientific article; zbMATH DE number 6021220