On Generalized Class of Bell Polynomials Associated with Geometric Applications
In this paper, we introduce a new class of special polynomials called the generalized Bell polynomials, constructed by combining two-variable general polynomials with two-variable Bell polynomials. The concept of the monomiality principle was employed to establish the generating function and obtain...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/2/73 |
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| author | Rashad A. Al-Jawfi Abdulghani Muhyi Wadia Faid Hassan Al-shameri |
| author_facet | Rashad A. Al-Jawfi Abdulghani Muhyi Wadia Faid Hassan Al-shameri |
| author_sort | Rashad A. Al-Jawfi |
| collection | DOAJ |
| description | In this paper, we introduce a new class of special polynomials called the generalized Bell polynomials, constructed by combining two-variable general polynomials with two-variable Bell polynomials. The concept of the monomiality principle was employed to establish the generating function and obtain various results for these polynomials. We explore certain related identities, properties, as well as differential and integral formulas. Further, specific members within the generalized Bell family—such as the Gould-Hopper-Bell polynomials, Laguerre-Bell polynomials, truncated-exponential-Bell polynomials, Hermite-Appell-Bell polynomials, and Fubini-Bell polynomials—were examined, unveiling analogous outcomes for each. Finally, <i>Mathematica</i> was utilized to investigate the zero distributions of the Gould-Hopper-Bell polynomials. |
| first_indexed | 2024-03-07T22:42:36Z |
| format | Article |
| id | doaj.art-5bb16032b19f46239251428b38c37e71 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-07T22:42:36Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5bb16032b19f46239251428b38c37e712024-02-23T15:07:20ZengMDPI AGAxioms2075-16802024-01-011327310.3390/axioms13020073On Generalized Class of Bell Polynomials Associated with Geometric ApplicationsRashad A. Al-Jawfi0Abdulghani Muhyi1Wadia Faid Hassan Al-shameri2Department of Mathematics, Faculty of Sciences and Arts, Najran University, Najran 55461, Saudi ArabiaDepartment of Mathematics, Hajjah University, Hajjah, YemenDepartment of Mathematics, Faculty of Sciences and Arts, Najran University, Najran 55461, Saudi ArabiaIn this paper, we introduce a new class of special polynomials called the generalized Bell polynomials, constructed by combining two-variable general polynomials with two-variable Bell polynomials. The concept of the monomiality principle was employed to establish the generating function and obtain various results for these polynomials. We explore certain related identities, properties, as well as differential and integral formulas. Further, specific members within the generalized Bell family—such as the Gould-Hopper-Bell polynomials, Laguerre-Bell polynomials, truncated-exponential-Bell polynomials, Hermite-Appell-Bell polynomials, and Fubini-Bell polynomials—were examined, unveiling analogous outcomes for each. Finally, <i>Mathematica</i> was utilized to investigate the zero distributions of the Gould-Hopper-Bell polynomials.https://www.mdpi.com/2075-1680/13/2/73Bell polynomialstwo-variable general polynomialsgeneralized Bell polynomialsGould-Hopper-Bell polynomialsgenerating functionzero distribution |
| spellingShingle | Rashad A. Al-Jawfi Abdulghani Muhyi Wadia Faid Hassan Al-shameri On Generalized Class of Bell Polynomials Associated with Geometric Applications Axioms Bell polynomials two-variable general polynomials generalized Bell polynomials Gould-Hopper-Bell polynomials generating function zero distribution |
| title | On Generalized Class of Bell Polynomials Associated with Geometric Applications |
| title_full | On Generalized Class of Bell Polynomials Associated with Geometric Applications |
| title_fullStr | On Generalized Class of Bell Polynomials Associated with Geometric Applications |
| title_full_unstemmed | On Generalized Class of Bell Polynomials Associated with Geometric Applications |
| title_short | On Generalized Class of Bell Polynomials Associated with Geometric Applications |
| title_sort | on generalized class of bell polynomials associated with geometric applications |
| topic | Bell polynomials two-variable general polynomials generalized Bell polynomials Gould-Hopper-Bell polynomials generating function zero distribution |
| url | https://www.mdpi.com/2075-1680/13/2/73 |
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