Recurrent relations for the solutions of an infinite system of linear algebraic equations
We obtain recurrent relations for bounded solutions of the system of equations $$X_k - \sum\limits_{n = 0}^\infty {\frac{{(k + n)!}}{{k!n!}}} \alpha ^{k + n + 1} x_n = f_{k,} k = 0,1,..., \alpha \in (0,1/2),$$ with right-hand sides {f k } k=0 ∞ ={δ kj } k=0 ∞ ,j=0,1,..., where δ kj is the...
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| Date: | 1995 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5534 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511766398631936 |
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| author | Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. |
| author_facet | Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. |
| author_sort | Gomilko, A. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:12:51Z |
| description | We obtain recurrent relations for bounded solutions of the system of equations $$X_k - \sum\limits_{n = 0}^\infty {\frac{{(k + n)!}}{{k!n!}}} \alpha ^{k + n + 1} x_n = f_{k,} k = 0,1,..., \alpha \in (0,1/2),$$ with right-hand sides {f k } k=0 ∞ ={δ kj } k=0 ∞ ,j=0,1,..., where δ kj is the Kronecker symbol. |
| first_indexed | 2026-03-24T03:18:06Z |
| format | Article |
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| id | umjimathkievua-article-5534 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:18:06Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5c/de079efc98b95e1b6dcee42210c64f5c.pdf |
| spelling | umjimathkievua-article-55342020-03-19T09:12:51Z Recurrent relations for the solutions of an infinite system of linear algebraic equations Рекуррентные формулы для решений одной бесконечной системы линейных алгебраических уравнений Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. We obtain recurrent relations for bounded solutions of the system of equations $$X_k - \sum\limits_{n = 0}^\infty {\frac{{(k + n)!}}{{k!n!}}} \alpha ^{k + n + 1} x_n = f_{k,} k = 0,1,..., \alpha \in (0,1/2),$$ with right-hand sides {f k } k=0 ∞ ={δ kj } k=0 ∞ ,j=0,1,..., where δ kj is the Kronecker symbol. Знайдено рекурентні формули для обмежених розв'язків системи рівнянь $$X_k - \sum\limits_{n = 0}^\infty {\frac{{(k + n)!}}{{k!n!}}} \alpha ^{k + n + 1} x_n = f_{k,} k = 0,1,..., \alpha \in (0,1/2),$$ з правими частинами $\{f_k\}_{k = 0}^{ ∞} = \{δ_{kj} \}_{ k=0}^{ ∞}, \;j = 0,1,...$, де $δ_{kj} $- — символ Кронекера. Institute of Mathematics, NAS of Ukraine 1995-10-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5534 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 10 (1995); 1328–1332 Український математичний журнал; Том 47 № 10 (1995); 1328–1332 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5534/7756 https://umj.imath.kiev.ua/index.php/umj/article/view/5534/7757 Copyright (c) 1995 Gomilko A. M. |
| spellingShingle | Gomilko, A. M. Гомилко, А. М. Гомилко, А. М. Recurrent relations for the solutions of an infinite system of linear algebraic equations |
| title | Recurrent relations for the solutions of an infinite system of linear algebraic equations |
| title_alt | Рекуррентные формулы для решений одной бесконечной системы линейных алгебраических уравнений |
| title_full | Recurrent relations for the solutions of an infinite system of linear algebraic equations |
| title_fullStr | Recurrent relations for the solutions of an infinite system of linear algebraic equations |
| title_full_unstemmed | Recurrent relations for the solutions of an infinite system of linear algebraic equations |
| title_short | Recurrent relations for the solutions of an infinite system of linear algebraic equations |
| title_sort | recurrent relations for the solutions of an infinite system of linear algebraic equations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5534 |
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