A matrix approach to Sheffer polynomials

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• 作者：Lidia Aceto^a ; ^{lidia.aceto@unipi.it" class="auth_mail" title="E-mail the corresponding author} ; Isabel Caç ; ã ; o^b ; ¹ ; ^{isabel.cacao@ua.pt" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Sheffer polynomials ; Binomial type polynomials ; Appell polynomials ; Creation matrix ; Generalized Pascal matrix
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：87-100
• 全文大小：343 K

文摘

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.