منابع مشابه
Generalized Fibonacci and Lucas Polynomials and Their Associated Diagonal Polynomials
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 کاملDeterminants and permanents of Hessenberg matrices and generalized Lucas polynomials
In this paper, we give some determinantal and permanental representations of generalized Lucas polynomials, which are a general form of generalized bivariate Lucas p-polynomials, ordinary Lucas and Perrin sequences etc., by using various Hessenberg matrices. In addition, we show that determinant and permanent of these Hessenberg matrices can be obtained by using combinations. Then we show, the ...
متن کاملOn the K–order Derivative Sequences of Generalized Fibonacci and Lucas Polynomials
In this note we consider two classes of polynomials Un and Vn. These polynomials are special cases of Un,m and Vn,m (see [2]), respectively. Also, Un and Vn are generalized Fibonacci and Lucas polynomials. In fact, in this paper we study the polynomials Un,3 and Vn,3, together with their k−derivative sequences U (k) n and V (k) n . Some interesting identities are proved in the paper, for Un, Vn...
متن کاملOn convolved generalized Fibonacci and Lucas polynomials
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...
متن کاملOn Bivariate Complex Fibonacci and Lucas Polynomials
In this study we define and study the Bivariate Complex Fibonacci and Bivariate Complex Lucas Polynomials. We give generating function, Binet formula, explicit formula and partial derivation of these polynomials. By defining these bivariate polynomials for special cases Fn(x, 1) is the complex Fibonacci polynomials and Fn(1, 1) is the complex Fibonacci numbers. Finally in the last section we gi...
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ژورنال
عنوان ژورنال: Turkish Journal of Analysis and Number Theory
سال: 2016
ISSN: 2333-1100
DOI: 10.12691/tjant-3-2-3