Some Families of Differential Equations Associated with Multivariate Hermite Polynomials
In this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using the factorization approach. Families of differential equations, including differential, integro–differential, and partial differential equations, are obtained using these operators. T...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/5/390 |
| _version_ | 1797600014666563584 |
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| author | Badr Saad T. Alkahtani Ibtehal Alazman Shahid Ahmad Wani |
| author_facet | Badr Saad T. Alkahtani Ibtehal Alazman Shahid Ahmad Wani |
| author_sort | Badr Saad T. Alkahtani |
| collection | DOAJ |
| description | In this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using the factorization approach. Families of differential equations, including differential, integro–differential, and partial differential equations, are obtained using these operators. The Volterra integral for these polynomials is also discovered. |
| first_indexed | 2024-03-11T03:42:29Z |
| format | Article |
| id | doaj.art-44a8a1a3a5644dbba9d05c468a772840 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T03:42:29Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-44a8a1a3a5644dbba9d05c468a7728402023-11-18T01:26:27ZengMDPI AGFractal and Fractional2504-31102023-05-017539010.3390/fractalfract7050390Some Families of Differential Equations Associated with Multivariate Hermite PolynomialsBadr Saad T. Alkahtani0Ibtehal Alazman1Shahid Ahmad Wani2Department of Mathematics, College of Science, King Saud University, Riyadh 11989, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi ArabiaDepartment of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed University) (SIU), Pune 412115, IndiaIn this article, the recurrence relations and shift operators for multivariate Hermite polynomials are derived using the factorization approach. Families of differential equations, including differential, integro–differential, and partial differential equations, are obtained using these operators. The Volterra integral for these polynomials is also discovered.https://www.mdpi.com/2504-3110/7/5/390Hermite polynomialsrecurrence relationshift operatorsdifferential equationsintegral equation |
| spellingShingle | Badr Saad T. Alkahtani Ibtehal Alazman Shahid Ahmad Wani Some Families of Differential Equations Associated with Multivariate Hermite Polynomials Fractal and Fractional Hermite polynomials recurrence relation shift operators differential equations integral equation |
| title | Some Families of Differential Equations Associated with Multivariate Hermite Polynomials |
| title_full | Some Families of Differential Equations Associated with Multivariate Hermite Polynomials |
| title_fullStr | Some Families of Differential Equations Associated with Multivariate Hermite Polynomials |
| title_full_unstemmed | Some Families of Differential Equations Associated with Multivariate Hermite Polynomials |
| title_short | Some Families of Differential Equations Associated with Multivariate Hermite Polynomials |
| title_sort | some families of differential equations associated with multivariate hermite polynomials |
| topic | Hermite polynomials recurrence relation shift operators differential equations integral equation |
| url | https://www.mdpi.com/2504-3110/7/5/390 |
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