Generalized Lucas polynomials and relationships between the Fibonacci polynomials and Lucas polynomials
| Autor: | Engin Özkan, İpek Altun |
|---|---|
| Přispěvatelé: | EBYÜ, Fen Edebiyat Fakültesi |
| Rok vydání: | 2019 |
| Předmět: |
Algebra and Number Theory
Fibonacci number Mathematics::General Mathematics Mathematics::Number Theory Mathematics::History and Overview 010102 general mathematics Fibonacci numbers 010103 numerical & computational mathematics Lucas numbers 01 natural sciences Combinatorics Lucas number Lucas polynomials Fibonacci polynomials 0101 mathematics Mathematics |
| Zdroj: | Communications in Algebra. 47:4020-4030 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2019.1576186 |
| Popis: | Fibonacci numbers and sequence applications are of great interest. The Fibonacci sequence appears in many branches of mathematics. These include group theory, calculus, applied mathematics, linear algebra, etc. Also, these numbers have many important applications to diverse fields such as computer science, physics, biology and statistics. We can see applications of the Fibonacci sequence in group theory in [3, 8] and also see some generalized Fibonacci and Lucas sequences in [1, 2, 4, 7, 9, 10, 13–15, 17]. We can see some applications of the Fibonacci polynomials in [5, 6, 16, 18, 19]. One of the researches in this area is that Hoggatt and Bicknell study on the Fibonacci polynomials and nstep Fibonacci polynomials and give some properties of the polynomials [11]. In this article, we find elements of the Lucas polynomials by aid of a new matrix and the generalized u-matrix investigated by Ivie [12]. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are generalized in the paper. Also, we give relationships between the Fibonacci polynomials and the Lucas polynomials. Let us give the Fibonacci polynomials in [11] before we give the Lucas polynomials. In this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are generalized in the paper. Furthermore, we give relationships between the Fibonacci polynomials and the Lucas polynomials. |
| Databáze: | OpenAIRE |
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