We obtain some new identities for the generalized Fibonacci polynomial by a approach, namely, Q(x) matrix.
 These including Cassini type identity and Honsberger formula can be applied to polynomial
 sequences such as polynomials, Lucas Pell Pell-Lucas polynomials so on, which
 generalize previous results in references.

The goal of this study is to develop some new connection formulae between two generalized classes Fibonacci and Lucas polynomials. Hypergeometric functions the kind 2F1(z) are included in all coefficients for a specific z. Several famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, Fermat–Lucas deduced special cases derived formulae. Some introduced generalize those existing...

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...

Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric have been studied in the literature with help generating functions their functional equations. In this paper, using (p,q)–Fibonacci (p,q)–Lucas Changhee numbers, we define (p,q)–Fibonacci–Changhee polynomials (p,q)–Lucas–Changhee respectively. We obtain some important identities relations these new...

Many properties of special polynomials, such as recurrence relations, sum formulas, and symmetric properties, have been studied in the literature with help generating functions their functional equations. In this paper, we define generalized (p,q)-Bernoulli–Fibonacci (p,q)-Bernoulli–Lucas polynomials numbers by using (p,q)-Bernoulli numbers, unified h(x)-Fibonacci h(x)-Lucas polynomials. We als...

In this paper, we investigate the generalized Tribonacci polynomials and deal with, in detail, two special cases which call them (r,s,t)-Tribonacci (r,s,t)-Tribonacci-Lucas polynomials. We also introduce a new sequence its namely co-Tribonacci, (r,s,t)-co-Tribonacci (r,s,t)-co-Tribonacci-Lucas polynomials, respectively. present Binet's formulas, generating functions, Simson summation formulas f...

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...