Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials
A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions. This paper presents research on a novel family of multivariate Hermite polynomials associated with Apostol-type Frobenius–Euler polynomia...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3439 |
| _version_ | 1827729365891284992 |
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| author | Mohra Zayed Shahid Ahmad Wani Yamilet Quintana |
| author_facet | Mohra Zayed Shahid Ahmad Wani Yamilet Quintana |
| author_sort | Mohra Zayed |
| collection | DOAJ |
| description | A comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions. This paper presents research on a novel family of multivariate Hermite polynomials associated with Apostol-type Frobenius–Euler polynomials. The study derives the generating expression, operational rule, differential equation, and other defining characteristics for these polynomials. Additionally, the monomiality principle for these polynomials is verified. Moreover, the research establishes series representations, summation formulae, and operational and symmetric identities, as well as recurrence relations satisfied by these polynomials. |
| first_indexed | 2024-03-10T23:46:50Z |
| format | Article |
| id | doaj.art-c3e0d6e2a87944ce8e680f488a23f776 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:46:50Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c3e0d6e2a87944ce8e680f488a23f7762023-11-19T02:02:00ZengMDPI AGMathematics2227-73902023-08-011116343910.3390/math11163439Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler PolynomialsMohra Zayed0Shahid Ahmad Wani1Yamilet Quintana2Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Lavale, Pune 412115, Maharashtra, IndiaDepartamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganés, 28911 Madrid, SpainA comprehensive framework has been developed to apply the monomiality principle from mathematical physics to various mathematical concepts from special functions. This paper presents research on a novel family of multivariate Hermite polynomials associated with Apostol-type Frobenius–Euler polynomials. The study derives the generating expression, operational rule, differential equation, and other defining characteristics for these polynomials. Additionally, the monomiality principle for these polynomials is verified. Moreover, the research establishes series representations, summation formulae, and operational and symmetric identities, as well as recurrence relations satisfied by these polynomials.https://www.mdpi.com/2227-7390/11/16/3439multivariate special polynomialsmonomiality principleexplicit formoperational connectionsymmetric identitiessummation formulae |
| spellingShingle | Mohra Zayed Shahid Ahmad Wani Yamilet Quintana Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials Mathematics multivariate special polynomials monomiality principle explicit form operational connection symmetric identities summation formulae |
| title | Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials |
| title_full | Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials |
| title_fullStr | Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials |
| title_full_unstemmed | Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials |
| title_short | Properties of Multivariate Hermite Polynomials in Correlation with Frobenius–Euler Polynomials |
| title_sort | properties of multivariate hermite polynomials in correlation with frobenius euler polynomials |
| topic | multivariate special polynomials monomiality principle explicit form operational connection symmetric identities summation formulae |
| url | https://www.mdpi.com/2227-7390/11/16/3439 |
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