A matrix approach to Sheffer polynomials

Lidia Aceto, Isabel Cação

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Abstract

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.

Lingua originaleInglese
pagine (da-a)87-100
Numero di pagine14
RivistaJournal of Mathematical Analysis and Applications
Volume446
Numero di pubblicazione1
DOI
Stato di pubblicazionePubblicato - 1 feb 2017
Pubblicato esternamente

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