Affiliation:
1. Department of Mathematics, University of St. Thomas, 2115 Summit Avenue, Saint Paul, MN 55105-1079, USA
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.
Cited by
11 articles.
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