On some properties of generalized Fibonacci and Lucas polynomials
نویسندگان
چکیده
منابع مشابه
On some properties on bivariate Fibonacci and Lucas polynomials
In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations.
متن کاملOn Some Properties of Bivariate Fibonacci and Lucas Polynomials
In this paper we generalize to bivariate Fibonacci and Lucas polynomials, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate bases are families of integers satisfying remarkable recurrence relations.
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We define the convolved hðxÞ-Fibonacci polynomials as an extension of the classical con-volved Fibonacci numbers. Then we give some combinatorial formulas involving the hðxÞ-Fibonacci and hðxÞ-Lucas polynomials. Moreover we obtain the convolved hðxÞ-Fibo-nacci polynomials from a family of Hessenberg matrices. Fibonacci numbers and their generalizations have many interesting properties and appli...
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Horadam [7], in a recent article, defined two sequences of polynomials Jn(x) and j„(x), the Jacobsthal and Jacobsthal-Lucas polynomials, respectively, and studied their properties. In the same article, he also defined and studied the properties of the rising and descending polynomials i^(x), rn(x), Dn(x)y and dn(x), which are fashioned in a manner similar to those for Chebyshev, Fermat, and oth...
متن کاملSome Generalized Fibonacci Polynomials
We introduce polynomial generalizations of the r-Fibonacci, r-Gibonacci, and rLucas sequences which arise in connection with two statistics defined, respectively, on linear, phased, and circular r-mino arrangements.
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ژورنال
عنوان ژورنال: An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
سال: 2017
ISSN: 2146-5703,2146-0957
DOI: 10.11121/ijocta.01.2017.00398