$d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations
UDC 517.5 We define $d$-Gaussian Fibonacci polynomials and $d$-Gaussian Lucas polynomials. We present the matrix representations of these polynomials. By using the Riordan method, we obtain the factorizations of the Pascal matrix including the polynomials...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6988 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512568946196480 |
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| author | Özkan, E. Uysal, M. Özkan, E. Uysal, M. |
| author_facet | Özkan, E. Uysal, M. Özkan, E. Uysal, M. |
| author_sort | Özkan, E. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-05-14T15:30:12Z |
| description |
UDC 517.5
We define $d$-Gaussian Fibonacci polynomials and $d$-Gaussian Lucas polynomials. We present the matrix representations of these polynomials. By using the Riordan method, we obtain the factorizations of the Pascal matrix including the polynomials. In addition, we define the infinite $d$-Gaussian Fibonacci polynomial matrix and the $d$-Gaussian Lucas polynomial matrix and give their inverses. |
| doi_str_mv | 10.37863/umzh.v75i4.6988 |
| first_indexed | 2026-03-24T03:30:52Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6988 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:30:52Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-69882023-05-14T15:30:12Z $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations Özkan, E. Uysal, M. Özkan, E. Uysal, M. d-Gaussian Fibonacci polynomials, d-Gaussian Lucas polynomials, Generating function Binet formula Riordan matrix. UDC 517.5 We define $d$-Gaussian Fibonacci polynomials and $d$-Gaussian Lucas polynomials. We present the matrix representations of these polynomials. By using the Riordan method, we obtain the factorizations of the Pascal matrix including the polynomials. In addition, we define the infinite $d$-Gaussian Fibonacci polynomial matrix and the $d$-Gaussian Lucas polynomial matrix and give their inverses. УДК 517.5 $d$-Гауссові поліноми Фібоначчі, $d$-гауссові  поліноми Лукаса та їхні матричні зображення Визначено $d$-гаусcові поліноми Фібоначчі та $d$-гаусcові поліноми Лукаса. Наведено матричні зображення цих поліномів. Використовуючи метод Ріордана,  отримaно факторизації матриці Паскаля, що включають поліноми. Крім того,  визначено нескінченну матрицю $d$-гаусcових поліномів Фібоначчі та матрицю $d$-гаусcових поліномів Лукаса і наведено їхні обернені матриці. Institute of Mathematics, NAS of Ukraine 2023-05-10 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6988 10.37863/umzh.v75i4.6988 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 4 (2023); 491 - 510 Український математичний журнал; Том 75 № 4 (2023); 491 - 510 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6988/9782 Copyright (c) 2023 Engin Özkan |
| spellingShingle | Özkan, E. Uysal, M. Özkan, E. Uysal, M. $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations |
| title | $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations |
| title_alt | $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations |
| title_full | $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations |
| title_fullStr | $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations |
| title_full_unstemmed | $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations |
| title_short | $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations |
| title_sort | $d$-gaussian fibonacci, $d$-gaussian lucas polynomials and their matrix representations |
| topic_facet | d-Gaussian Fibonacci polynomials, d-Gaussian Lucas polynomials, Generating function Binet formula Riordan matrix. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6988 |
| work_keys_str_mv | AT ozkane dgaussianfibonaccidgaussianlucaspolynomialsandtheirmatrixrepresentations AT uysalm dgaussianfibonaccidgaussianlucaspolynomialsandtheirmatrixrepresentations AT ozkane dgaussianfibonaccidgaussianlucaspolynomialsandtheirmatrixrepresentations AT uysalm dgaussianfibonaccidgaussianlucaspolynomialsandtheirmatrixrepresentations |