منابع مشابه
On 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 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).
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...
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: International Journal of Advanced Mathematical Sciences
سال: 2013
ISSN: 2307-454X
DOI: 10.14419/ijams.v2i1.1388