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 |
| Published: |
MDPI AG
2023-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/12/2113 |
| Summary: | 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. |
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| ISSN: | 2073-8994 |