Differential Equation and Recursive Formulas of Sheffer Polynomial Sequences. (3rd November 2011)

• Record Type: Journal Article
• Authors: Youn Youn, Heekyung Heekyung; Yang Yang, Yongzhi Yongzhi
• Other Names: Chlebík Chlebík M. M. Academic Editor.; Eriksson Eriksson K. K. Academic Editor.; Wilson Wilson M. C. M. C. Academic Editor.
• Is Part Of: ISRN discrete mathematics. Volume 2011(2011)
• Publication Date: 2011-11-03
• Subjects: Discrete mathematics -- Periodicals; Computer science -- Mathematics; Computer science -- Mathematics; Periodicals; 511.1
• DOI: 10.5402/2011/476462
• Languages: English
• ISSNs: 2090-7788

Abstract

Abstract : 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 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 He and Ricci's work (2002) to a broader class of polynomial sequences, from Appell to Sheffer, using a different method. The work is self-contained.