A Note on Incomplete Fibonacci–Lucas Relations
We define the incomplete generalized bivariate Fibonacci <i>p</i>-polynomials and the incomplete generalized bivariate Lucas <i>p</i>-polynomials. We study their recursive relations and derive an interesting relationship through their generating functions. Subsequently, we pr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/12/2113 |
| _version_ | 1797379292942827520 |
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| author | Jingyang Zhong Jialing Yao Chan-Liang Chung |
| author_facet | Jingyang Zhong Jialing Yao Chan-Liang Chung |
| author_sort | Jingyang Zhong |
| collection | DOAJ |
| description | We define the incomplete generalized bivariate Fibonacci <i>p</i>-polynomials and the incomplete generalized bivariate Lucas <i>p</i>-polynomials. We study their recursive relations and derive an interesting relationship through their generating functions. Subsequently, we prove an incomplete version of the well-known Fibonacci–Lucas relation and make some extensions to the relation involving incomplete generalized bivariate Fibonacci and Lucas <i>p</i>-polynomials. An argument about going from the regular to the incomplete Fibonacci–Lucas relation is discussed. We provide a relation involving the incomplete Leonardo and the incomplete Lucas–Leonardo <i>p</i>-numbers as an illustration. |
| first_indexed | 2024-03-08T20:20:03Z |
| format | Article |
| id | doaj.art-727867acc45542d0b1e03d0abe5ba6b6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T20:20:03Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-727867acc45542d0b1e03d0abe5ba6b62023-12-22T14:45:05ZengMDPI AGSymmetry2073-89942023-11-011512211310.3390/sym15122113A Note on Incomplete Fibonacci–Lucas RelationsJingyang Zhong0Jialing Yao1Chan-Liang Chung2School of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, ChinaSchool of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, ChinaSchool of Mathematics and Statistics, Fuzhou University, Fuzhou 350108, ChinaWe define the incomplete generalized bivariate Fibonacci <i>p</i>-polynomials and the incomplete generalized bivariate Lucas <i>p</i>-polynomials. We study their recursive relations and derive an interesting relationship through their generating functions. Subsequently, we prove an incomplete version of the well-known Fibonacci–Lucas relation and make some extensions to the relation involving incomplete generalized bivariate Fibonacci and Lucas <i>p</i>-polynomials. An argument about going from the regular to the incomplete Fibonacci–Lucas relation is discussed. We provide a relation involving the incomplete Leonardo and the incomplete Lucas–Leonardo <i>p</i>-numbers as an illustration.https://www.mdpi.com/2073-8994/15/12/2113Fibonacci–Lucas relationbivariate Fibonacci p-polynomialsincomplete generalized bivariate Fibonacci p-polynomials |
| spellingShingle | Jingyang Zhong Jialing Yao Chan-Liang Chung A Note on Incomplete Fibonacci–Lucas Relations Symmetry Fibonacci–Lucas relation bivariate Fibonacci p-polynomials incomplete generalized bivariate Fibonacci p-polynomials |
| title | A Note on Incomplete Fibonacci–Lucas Relations |
| title_full | A Note on Incomplete Fibonacci–Lucas Relations |
| title_fullStr | A Note on Incomplete Fibonacci–Lucas Relations |
| title_full_unstemmed | A Note on Incomplete Fibonacci–Lucas Relations |
| title_short | A Note on Incomplete Fibonacci–Lucas Relations |
| title_sort | note on incomplete fibonacci lucas relations |
| topic | Fibonacci–Lucas relation bivariate Fibonacci p-polynomials incomplete generalized bivariate Fibonacci p-polynomials |
| url | https://www.mdpi.com/2073-8994/15/12/2113 |
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