On generalized Hermite polynomials
This article is devoted to establishing new formulas concerning generalized Hermite polynomials (GHPs) that generalize the classical Hermite polynomials. Derivative expressions of these polynomials that involve one parameter are found in terms of other parameter polynomials. Some other important for...
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| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241556?viewType=HTML |
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| author | Waleed Mohamed Abd-Elhameed Omar Mazen Alqubori |
| author_facet | Waleed Mohamed Abd-Elhameed Omar Mazen Alqubori |
| author_sort | Waleed Mohamed Abd-Elhameed |
| collection | DOAJ |
| description | This article is devoted to establishing new formulas concerning generalized Hermite polynomials (GHPs) that generalize the classical Hermite polynomials. Derivative expressions of these polynomials that involve one parameter are found in terms of other parameter polynomials. Some other important formulas, such as the linearization and connection formulas between these polynomials and some other polynomials, are also given. Most of the coefficients are represented in terms of hypergeometric functions that can be reduced in some specific cases using some standard formulas. Two applications of the developed formulas in this paper are given. The first application is concerned with introducing some weighted definite integrals involving the GHPs. In contrast, the second is concerned with establishing the operational matrix of the integer derivatives of the GHPs. |
| format | Article |
| id | doaj-art-be3a30fc6b684223b8e8ceee5526e843 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-be3a30fc6b684223b8e8ceee5526e8432025-08-20T02:27:49ZengAIMS PressAIMS Mathematics2473-69882024-11-01911324633249010.3934/math.20241556On generalized Hermite polynomialsWaleed Mohamed Abd-Elhameed 0Omar Mazen Alqubori11. Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi Arabia 2. Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt1. Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaThis article is devoted to establishing new formulas concerning generalized Hermite polynomials (GHPs) that generalize the classical Hermite polynomials. Derivative expressions of these polynomials that involve one parameter are found in terms of other parameter polynomials. Some other important formulas, such as the linearization and connection formulas between these polynomials and some other polynomials, are also given. Most of the coefficients are represented in terms of hypergeometric functions that can be reduced in some specific cases using some standard formulas. Two applications of the developed formulas in this paper are given. The first application is concerned with introducing some weighted definite integrals involving the GHPs. In contrast, the second is concerned with establishing the operational matrix of the integer derivatives of the GHPs.https://www.aimspress.com/article/doi/10.3934/math.20241556?viewType=HTMLgeneralized hermite polynomialshypergeometric functionsconnectionlinearization formulashigh-order derivatives |
| spellingShingle | Waleed Mohamed Abd-Elhameed Omar Mazen Alqubori On generalized Hermite polynomials AIMS Mathematics generalized hermite polynomials hypergeometric functions connection linearization formulas high-order derivatives |
| title | On generalized Hermite polynomials |
| title_full | On generalized Hermite polynomials |
| title_fullStr | On generalized Hermite polynomials |
| title_full_unstemmed | On generalized Hermite polynomials |
| title_short | On generalized Hermite polynomials |
| title_sort | on generalized hermite polynomials |
| topic | generalized hermite polynomials hypergeometric functions connection linearization formulas high-order derivatives |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241556?viewType=HTML |
| work_keys_str_mv | AT waleedmohamedabdelhameed ongeneralizedhermitepolynomials AT omarmazenalqubori ongeneralizedhermitepolynomials |