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...
| 出版年: | Ural Mathematical Journal |
|---|---|
| 主要な著者: | , |
| フォーマット: | 論文 |
| 言語: | 英語 |
| 出版事項: |
Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2022-12-01
|
| 主題: | |
| オンライン･アクセス: | https://umjuran.ru/index.php/umj/article/view/528 |
| 要約: | 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. |
|---|---|
| ISSN: | 2414-3952 |