BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS
In this paper, we introduce the concept of the \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials, where \(\mathbb{B}_{\alpha}\) is the raising operator \(\mathbb{B}_{\alpha}:=x^2 \cdot {d}/{dx}+\big(2(\alpha-1)x+1\big)\mathbb{I}\), with nonzero complex number \(\alpha\) and \(\mathbb{I}\) rep...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.
2022-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/528 |
| _version_ | 1797971209574416384 |
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| author | Baghdadi Aloui Jihad Souissi |
| author_facet | Baghdadi Aloui Jihad Souissi |
| author_sort | Baghdadi Aloui |
| collection | DOAJ |
| description | In this paper, we introduce the concept of the \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials, where \(\mathbb{B}_{\alpha}\) is the raising operator \(\mathbb{B}_{\alpha}:=x^2 \cdot {d}/{dx}+\big(2(\alpha-1)x+1\big)\mathbb{I}\), with nonzero complex number \(\alpha\) and \(\mathbb{I}\) representing the identity operator. We show that the Bessel polynomials \(B^{(\alpha)}_n(x),\ n\geq0\), where \(\alpha\neq-{m}/{2}, \ m\geq -2, \ m\in \mathbb{Z}\), are the only \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials. As an application, we present some new formulas for polynomial solution. |
| first_indexed | 2024-04-11T03:29:01Z |
| format | Article |
| id | doaj.art-65ad8617b1534f8fbf6c4e4fcf090cff |
| institution | Directory Open Access Journal |
| issn | 2414-3952 |
| language | English |
| last_indexed | 2024-04-11T03:29:01Z |
| publishDate | 2022-12-01 |
| publisher | Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin. |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj.art-65ad8617b1534f8fbf6c4e4fcf090cff2023-01-02T06:52:22ZengKrasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin.Ural Mathematical Journal2414-39522022-12-018210.15826/umj.2022.2.001166BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORSBaghdadi Aloui0Jihad Souissi1University of Gabes, Higher Institute of Industrial Systems of Gabes Salah Eddine Elayoubi Str., 6033 GabesUniversity of Gabes, Faculty of Sciences of Gabes Erriadh Str., 6072 GabesIn this paper, we introduce the concept of the \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials, where \(\mathbb{B}_{\alpha}\) is the raising operator \(\mathbb{B}_{\alpha}:=x^2 \cdot {d}/{dx}+\big(2(\alpha-1)x+1\big)\mathbb{I}\), with nonzero complex number \(\alpha\) and \(\mathbb{I}\) representing the identity operator. We show that the Bessel polynomials \(B^{(\alpha)}_n(x),\ n\geq0\), where \(\alpha\neq-{m}/{2}, \ m\geq -2, \ m\in \mathbb{Z}\), are the only \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials. As an application, we present some new formulas for polynomial solution.https://umjuran.ru/index.php/umj/article/view/528classical orthogonal polynomials, linear functionals, bessel polynomials, raising operators, connection formulas |
| spellingShingle | Baghdadi Aloui Jihad Souissi BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS Ural Mathematical Journal classical orthogonal polynomials, linear functionals, bessel polynomials, raising operators, connection formulas |
| title | BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS |
| title_full | BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS |
| title_fullStr | BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS |
| title_full_unstemmed | BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS |
| title_short | BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS |
| title_sort | bessel polynomials and some connection formulas in terms of the action of linear differential operators |
| topic | classical orthogonal polynomials, linear functionals, bessel polynomials, raising operators, connection formulas |
| url | https://umjuran.ru/index.php/umj/article/view/528 |
| work_keys_str_mv | AT baghdadialoui besselpolynomialsandsomeconnectionformulasintermsoftheactionoflineardifferentialoperators AT jihadsouissi besselpolynomialsandsomeconnectionformulasintermsoftheactionoflineardifferentialoperators |