Lucas-type associated polynomials. (English) Zbl 07885200
Summary: In this paper, we define a new type of Lucas polynomials known as Lucas-type associated polynomials and investigate their fundamental properties and identities. An interesting formula for Lucas-type associated polynomials can be derived using Leibniz’s rule for derivatives, defined by Rodrigue’s Lucas-type formula. Additionally, we establish an integral connection between Lucas-type associated polynomials and associated Fibonacci polynomials.
MSC:
| 05A19 | Combinatorial identities, bijective combinatorics |
| 11B83 | Special sequences and polynomials |
Keywords:
Fibonacci polynomials; Lucas polynomials; associated Lucas polynomials; explicit formulas; generating functionsReferences:
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| [2] | G. Guettai, D. Laissaoui, and M. Rahmani. On associated Fibonacci polynomials , 2021. Submitted. |
| [3] | G. Guettai, D. Laissaoui, and M. Rahmani. Generalized Laguerre transforms of sequences. Creat. Math. Inform., 32(2):165-171, 2023. |
| [4] | T. Koshy. Fibonacci and Lucas numbers with applications. Pure and Applied Mathematics (New York). Wiley-Interscience, New York, 2001. · Zbl 0984.11010 |
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