Generalizations of the Fibonacci and Lucas polynomials
نویسندگان
چکیده
منابع مشابه
On 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...
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 کاملGeneralized 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 کاملOn the Expansion of Fibonacci and Lucas Polynomials
Recently, Belbachir and Bencherif have expanded Fibonacci and Lucas polynomials using bases of Fibonacci-and Lucas-like polynomials. Here, we provide simplified proofs for the expansion formulaethat in essence a computer can do. Furthermore, for 2 of the 5 instances, we find q-analogues.
متن کاملq-ANALOGS OF GENERALIZED FIBONACCI AND LUCAS POLYNOMIALS
The Fibonacci operator approach inspired by Andrews (2004) is explored to investigate q-analogs of the generalized Fibonacci and Lucas polynomials introduced by Chu and Vicenti (2003). Their generating functions are compactly expressed in terms of Fibonacci operator fractions. A determinant evaluation on q-binomial coefficients is also established which extends a recent result of Sun (2005).
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ژورنال
عنوان ژورنال: Filomat
سال: 2009
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil0903291d