Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials
By utilizing the generating function of higher-order Bernoulli polynomials, we uncover novel relationships that intertwine higher-order Bernoulli polynomials, higher-order Bernoulli numbers, Stirling numbers of the second kind, and central factorial numbers of the second kind. Leveraging these inter...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-02-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025148 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850216320076873728 |
|---|---|
| author | Aimin Xu |
| author_facet | Aimin Xu |
| author_sort | Aimin Xu |
| collection | DOAJ |
| description | By utilizing the generating function of higher-order Bernoulli polynomials, we uncover novel relationships that intertwine higher-order Bernoulli polynomials, higher-order Bernoulli numbers, Stirling numbers of the second kind, and central factorial numbers of the second kind. Leveraging these interconnections, we successfully rederive the identities formulated by Qi and Taylor, specifically those pertaining to Stirling numbers of the second kind and central factorial numbers of the second kind. Additionally, we derive series expansions for both positive integer and real powers of the sinc and sinhc functions. |
| format | Article |
| id | doaj-art-19a3e570a0204b098ea80800855f3ddc |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-19a3e570a0204b098ea80800855f3ddc2025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011023197320610.3934/math.2025148Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomialsAimin Xu0Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, ChinaBy utilizing the generating function of higher-order Bernoulli polynomials, we uncover novel relationships that intertwine higher-order Bernoulli polynomials, higher-order Bernoulli numbers, Stirling numbers of the second kind, and central factorial numbers of the second kind. Leveraging these interconnections, we successfully rederive the identities formulated by Qi and Taylor, specifically those pertaining to Stirling numbers of the second kind and central factorial numbers of the second kind. Additionally, we derive series expansions for both positive integer and real powers of the sinc and sinhc functions.https://www.aimspress.com/article/doi/10.3934/math.2025148bernoulli polynomialbernoulli numberseries expansioncentral factorial numbers of the second kindstirling numbers of the second kind |
| spellingShingle | Aimin Xu Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials AIMS Mathematics bernoulli polynomial bernoulli number series expansion central factorial numbers of the second kind stirling numbers of the second kind |
| title | Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials |
| title_full | Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials |
| title_fullStr | Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials |
| title_full_unstemmed | Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials |
| title_short | Some identities connecting Stirling numbers, central factorial numbers and higher-order Bernoulli polynomials |
| title_sort | some identities connecting stirling numbers central factorial numbers and higher order bernoulli polynomials |
| topic | bernoulli polynomial bernoulli number series expansion central factorial numbers of the second kind stirling numbers of the second kind |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025148 |
| work_keys_str_mv | AT aiminxu someidentitiesconnectingstirlingnumberscentralfactorialnumbersandhigherorderbernoullipolynomials |