Differential Equation and Recursive Formulas of Sheffer Polynomial Sequences. (3rd November 2011) - Youn Youn, Heekyung Heekyung; Yang Yang, Yongzhi Yongzhi
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.