Next Article in Journal
A Novel Empirical Interpolation Surrogate for Digital Twin Wave‑Based Structural Health Monitoring with MATLAB Implementation
Previous Article in Journal
Bilinear Learning with Dual-Chain Feature Attention for Multimodal Rumor Detection
Previous Article in Special Issue
Constrained Underdiagonal Paths and Pattern Avoiding Permutations
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Mathematics
Volume 13
Issue 11
10.3390/math13111732
mathematics-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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

by
Tian-Xiao He
1,* and
Emanuele Munarini
2
1
Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702, USA
2
Dipartimento di Matematica, Politecnico di Milano, 20133 Milan, Italy
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(11), 1732; https://doi.org/10.3390/math13111732
Submission received: 9 April 2025 / Revised: 13 May 2025 / Accepted: 22 May 2025 / Published: 24 May 2025
(This article belongs to the Special Issue Combinatorics, Riordan Matrices and Umbral Calculus—in Memory of Prof. Emanuele Munarini)
Versions Notes

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 Appell polynomials; Stirling numbers; harmonic numbers; q-binomial coefficients; q-Stirling numbers; Riordan-type arrays; sheffer-type matrices; symbolic method; umbral identities

Share and Cite

MDPI and ACS Style

He, T.-X.; Munarini, E. Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers. Mathematics 2025, 13, 1732. https://doi.org/10.3390/math13111732

AMA Style

He T-X, Munarini E. Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers. Mathematics. 2025; 13(11):1732. https://doi.org/10.3390/math13111732

Chicago/Turabian Style

He, Tian-Xiao, and Emanuele Munarini. 2025. "Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers" Mathematics 13, no. 11: 1732. https://doi.org/10.3390/math13111732

APA Style

He, T.-X., & Munarini, E. (2025). Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers. Mathematics, 13(11), 1732. https://doi.org/10.3390/math13111732

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop