Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers
In this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of <i>s</i>-Appell polynomials related to Stirling numbers and binomial coefficients. We discuss some properties of <i>s</i>...
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MDPI AG
2025-05-01
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| author | Tian-Xiao He Emanuele Munarini |
| author_facet | Tian-Xiao He Emanuele Munarini |
| author_sort | Tian-Xiao He |
| collection | DOAJ |
| description | In this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of <i>s</i>-Appell polynomials related to Stirling numbers and binomial coefficients. We discuss some properties of <i>s</i>-Appell polynomial sequences related to Riordan arrays, Sheffer matrices, and their <i>q</i> analogs. |
| format | Article |
| id | doaj-art-e11afb5dd51543ff9f875e3e17c3d150 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e11afb5dd51543ff9f875e3e17c3d1502025-08-20T02:23:00ZengMDPI AGMathematics2227-73902025-05-011311173210.3390/math13111732Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling NumbersTian-Xiao He0Emanuele Munarini1Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702, USADipartimento di Matematica, Politecnico di Milano, 20133 Milan, ItalyIn this paper, we present two symbolic methods, in particular, the method starting from the source identity, umbra identity, for constructing identities of <i>s</i>-Appell polynomials related to Stirling numbers and binomial coefficients. We discuss some properties of <i>s</i>-Appell polynomial sequences related to Riordan arrays, Sheffer matrices, and their <i>q</i> analogs.https://www.mdpi.com/2227-7390/13/11/1732Appell polynomialsStirling numbersharmonic numbers<i>q</i>-binomial coefficients<i>q</i>-Stirling numbersRiordan-type arrays |
| spellingShingle | Tian-Xiao He Emanuele Munarini Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers Mathematics Appell polynomials Stirling numbers harmonic numbers <i>q</i>-binomial coefficients <i>q</i>-Stirling numbers Riordan-type arrays |
| title | Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers |
| title_full | Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers |
| title_fullStr | Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers |
| title_full_unstemmed | Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers |
| title_short | Symbolic Methods Applied to a Class of Identities Involving Appell Polynomials and Stirling Numbers |
| title_sort | symbolic methods applied to a class of identities involving appell polynomials and stirling numbers |
| topic | Appell polynomials Stirling numbers harmonic numbers <i>q</i>-binomial coefficients <i>q</i>-Stirling numbers Riordan-type arrays |
| url | https://www.mdpi.com/2227-7390/13/11/1732 |
| work_keys_str_mv | AT tianxiaohe symbolicmethodsappliedtoaclassofidentitiesinvolvingappellpolynomialsandstirlingnumbers AT emanuelemunarini symbolicmethodsappliedtoaclassofidentitiesinvolvingappellpolynomialsandstirlingnumbers |