International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 54263, 15 pages
doi:10.1155/IJMMS/2006/54263

Linearization coefficients for Sheffer polynomial sets via lowering operators

Y. Ben Cheikh1 and H. Chaggara2

1Département de Mathématiques, Faculté des Sciences de Monastir, Université de Monastir, Monastir 5019, Tunisia
2Département de Préparation en Math-Physique, Institut Préparatoire aux Études d'Ingénieur de Monastir, Monastir 5019, Tunisia

Received 16 May 2005; Revised 2 March 2006; Accepted 12 March 2006

Copyright © 2006 Y. Ben Cheikh and H. Chaggara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The lowering operator σ associated with a polynomial set {Pn}n≥0 is an operator not depending on n and satisfying the relation σPn=nPn−1. In this paper, we express explicitly the linearization coefficients for polynomial sets of Sheffer type using the corresponding lowering operators. We obtain some well-known results as particular cases.