Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers

Tian-Xiao He () and Emanuele Munarini
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Tian-Xiao He: Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702, USA
Emanuele Munarini: Dipartimento di Matematica, Politecnico di Milano, 20133 Milan, Italy

Mathematics, 2025, vol. 13, issue 11, 1-27

Abstract: In this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of s -Appell polynomials related to Stirling numbers and binomial coefficients. We discuss some properties of s -Appell polynomial sequences related to Riordan arrays, Sheffer matrices, and their q analogs.

Keywords: Appell polynomials; Stirling numbers; harmonic numbers; q -binomial coefficients; q -Stirling numbers; Riordan-type arrays; sheffer-type matrices; symbolic method; umbral identities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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