A new approach to the construction of generalized classical polynomials
UDC 517.587 In this paper, we develop a new method for constructing generalized classical polynomials, primarily Hermite polynomials in the sense of A. Krall, J. Koekoek, R. Koekoek, H. Bavinck, L. Littlejohn, et al. We construct a differential operator of infinite order whose eigenfunctions are suc...
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| Date: | 2021 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6256 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.587
In this paper, we develop a new method for constructing generalized classical polynomials, primarily Hermite polynomials in the sense of A. Krall, J. Koekoek, R. Koekoek, H. Bavinck, L. Littlejohn, et al. We construct a differential operator of infinite order whose eigenfunctions are such polynomials. For generalized Hermite polynomials, we investigate a number of properties inherent in classical orthogonal polynomials (orthogonality, generalized Rodrigues formula, three-term recurrence relation forming a function). The versatility of the method is revealed in constructing generalized Legendre and Chebyshev polynomials of the first kind. |
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| DOI: | 10.37863/umzh.v73i6.6256 |