Generalization of resonance equations for the Laguerre- and Legendre-type polynomials to the fourth-order equations
UDC 517.587 A recurrent algorithm for finding particular solutions of а fourth-order resonance equation connected with the generalization of Laguerre and Legendre polynomials is constructed and substantiated. For this purpose, we use the general theorem on the representation of partial solutions of...
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| Datum: | 2026 |
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| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1533 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860507326479335424 |
|---|---|
| author | Bandyrskii, B. I. Makarov, V. L. Romaniuk, N. M. Бандирський, Б. Й. Макаров, В. Л. Романюк, Н. М. |
| author_facet | Bandyrskii, B. I. Makarov, V. L. Romaniuk, N. M. Бандирський, Б. Й. Макаров, В. Л. Романюк, Н. М. |
| author_sort | Bandyrskii, B. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-02-09T14:27:57Z |
| description | UDC 517.587
A recurrent algorithm for finding particular solutions of а fourth-order resonance equation connected with the generalization of Laguerre and Legendre polynomials is constructed and substantiated. For this purpose, we use the general theorem on the representation of partial solutions of resonance equations in Banach spaces, which was proved by V. L. Makarov in 1976. An example of general solution to the resonant equations with a differential operator for the Laguerre-type polynomials is presented. |
| doi_str_mv | 10.3842/umzh.v71i11.1533 |
| first_indexed | 2026-03-24T02:07:32Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-1533 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T02:07:32Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/4a/15fed320fd8c2b52ee8afb1aaff89e4a |
| spelling | umjimathkievua-article-15332026-02-09T14:27:57Z Generalization of resonance equations for the Laguerre- and Legendre-type polynomials to the fourth-order equations Узагальнення резонансних рівнянь для поліномів типу Лагерра і Лежандра на рівняння четвертого порядку Bandyrskii, B. I. Makarov, V. L. Romaniuk, N. M. Бандирський, Б. Й. Макаров, В. Л. Романюк, Н. М. UDC 517.587 A recurrent algorithm for finding particular solutions of а fourth-order resonance equation connected with the generalization of Laguerre and Legendre polynomials is constructed and substantiated. For this purpose, we use the general theorem on the representation of partial solutions of resonance equations in Banach spaces, which was proved by V. L. Makarov in 1976. An example of general solution to the resonant equations with a differential operator for the Laguerre-type polynomials is presented. УДК 517.587 Побудовано й обґрунтовано рекурентний алгоритм знаходження частинних розв'язків резонансного рівняння четвертого порядку, пов'язаного з узагальненням поліномів Лагерра і Лежандра. Для цього використано загальну теорему про зображення частинних розв'язків резонансних рівнянь у банахових просторах, доведену В. Л. Макаровим у 1976 р. Наведено приклад загального розв'язку резонансних рівнянь із диференціальним оператором для поліномів типу Лагерра. Institute of Mathematics, NAS of Ukraine 2026-02-09 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/1533 10.3842/umzh.v71i11.1533 Ukrains’kyi Matematychnyi Zhurnal; Vol. 71 No. 11 (2019); 1529-1538 Український математичний журнал; Том 71 № 11 (2019); 1529-1538 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/1533/515 Copyright (c) 2019 Bandyrskii B. I.; Makarov V. L.; Romaniuk N. M. |
| spellingShingle | Bandyrskii, B. I. Makarov, V. L. Romaniuk, N. M. Бандирський, Б. Й. Макаров, В. Л. Романюк, Н. М. Generalization of resonance equations for the Laguerre- and Legendre-type polynomials to the fourth-order equations |
| title | Generalization of resonance equations for the
Laguerre- and Legendre-type polynomials to the fourth-order equations |
| title_alt | Узагальнення резонансних рівнянь для поліномів типу Лагерра і Лежандра на рівняння четвертого порядку |
| title_full | Generalization of resonance equations for the
Laguerre- and Legendre-type polynomials to the fourth-order equations |
| title_fullStr | Generalization of resonance equations for the
Laguerre- and Legendre-type polynomials to the fourth-order equations |
| title_full_unstemmed | Generalization of resonance equations for the
Laguerre- and Legendre-type polynomials to the fourth-order equations |
| title_short | Generalization of resonance equations for the
Laguerre- and Legendre-type polynomials to the fourth-order equations |
| title_sort | generalization of resonance equations for the
laguerre- and legendre-type polynomials to the fourth-order equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1533 |
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