Differential equation and recursive formulas of Sheffer polynomial sequences
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.
recursive formulas of Sheffer polynomial sequences
scientific article; zbMATH DE number 6021220