Recurrence relation for the Appell sequences

In this paper, we present several explicit formulas for Appell polynomials in terms of the weighted Stirling numbers of the second kind. We also provide a unified approach to obtain a three-term recurrence formula for the computation of Appell polynomials. Several examples are given to illustrate ou...

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Bibliographic Details
Published in:Integral transforms and special functions 2023-05, Vol.34 (5), p.414-429
Main Authors: Guettai, Ghania, Laissaoui, Diffalah, Rahmani, Mourad, Sebaoui, Madjid
Format: Article
Language:English
Subjects:
Appell sequences
Combinatorial analysis
explicit formulas
Polynomials
recurrence relations
weighted Stirling numbers
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Summary:In this paper, we present several explicit formulas for Appell polynomials in terms of the weighted Stirling numbers of the second kind. We also provide a unified approach to obtain a three-term recurrence formula for the computation of Appell polynomials. Several examples are given to illustrate our results. As an application, we define and study a new class of polynomials that we call SPI polynomials. They are related to sums of powers of integers.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2022.2140800