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...

In 1991 Ferri, Faccio and D’Amico introduced and investigated two numerical triangles, called the DFF and DFFz triangles. Later Trzaska also considered the DFF triangle. And in 1994 Jeannin generalized the two triangles. In this paper, we focus our attention on the generalized Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas polynomials, and several numerical triangles deduce...

This paper deals with the Catalan, Hankel, binomial transforms of generalized bivariate Fibonacci and Lucas polynomials. Also, some useful results such as generating functions, Binet formulas, summations defined by using recurrence relations these special polynomials are presented. Furthermore, certain important among deduced obtained new formulas. Finally, Catalan Cassini formulas for also der...

In this paper, we introduce the incomplete Vieta–Pell and Vieta–Pell–Lucas polynomials. We give some properties, recurrence relations generating function of these polynomials with suggestions for further research.

In this paper, we investigate the generalized Fibonacci (Horadam) polynomials and deal with, in detail, two special cases which call them $(r,s)$-Fibonacci $(r,s)$-Lucas polynomials. We present Binet's formulas, generating functions, Simson's summation formulas for these polynomial sequences. Moreover, give some identities matrices associated with Finally, several expressions combinatorial resu...

We characterize decomposition over C of polynomials fn(x) defined by the generalized Dicksontype recursive relation f0(x) = B, f1(x) = x, fn+1(x) = xfn(x)− afn−1(x) (n ≥ 1), where B, a ∈ Q or R. This parametric class of polynomials includes Fibonacci, Pell, Fermat, Dickson, Lucas (w-), Pell-Lucas, Fermat-Lucas polynomials as well as Chebyshev polynomials of the first and second kind. As an appl...

In this paper we construct two types of Hessenberg matrices with the property that every weighted isobaric polynomial (WIP) appears as a determinant of one of them, and as the permanent of the other. Every integer sequence which is linearly recurrent is representable by (an evaluation of) some linearly recurrent sequence of WIPs. WIPs are symmetric polynomials written in the elementary symmetri...

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).