A matrix approach to Sheffer polynomials

作者：Aceto Lidia^*; Cacao Isabel

来源：Journal of Mathematical Analysis and Applications, 2017, 446(1): 87-100.

DOI：10.1016/j.jmaa.2016.08.038

• Sheffer polynomials
• Binomial type polynomials
• Appell polynomials
• Creation matrix
• Generalized Pascal matrix

This paper deals with a unified matrix representation for the Sheffer polynomials. The core of the proposed approach is the so-called creation matrix, a special subdiagonal matrix having as nonzero entries positive integer numbers, whose exponential coincides with the well-known Pascal matrix. In fact, Sheffer polynomials may be expressed in terms of two matrices both connected to it. As we will show, one of them is strictly related to Appell polynomials, while the other is linked to a binomial type sequence. Consequently, different types of Sheffer polynomials correspond to different choices of these two matrices.

• 出版日期2017-2-1