On the norms of some special matrices with the harmonic fibonacci numbers

The aim of this paper is to study norms of some circulant matrices and some special matrices, which entries consist of harmonic Fibonacci numbers. © 2015, Gazi University Eti Mahallesi. All rights reserved

New families of generating functions for Q-fibonacci and the related polynomials

In this paper, several families of multilinear and multilateral generating functions for Fibonacci and Lucas polynomials based on g-integers are derived. Then some special cases are given. © 2018 Charles Babbage Research Centre. All rights reserved

On the bicomplex generalized tribonacci quaternions

In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet's formula, generating functions, and the summation formula for this type of quaternion are given. Lastly, as an application, we present the determinant of a special matrix, and we show that the determinant is equal to the nth term of the bicomplex generalized tribonacci quaternions. © 2019 by the author

A closed formula for the Horadam polynomials in terms of a tridiagonal determinant

In this paper, the authors present a closed formula for the Horadam polynomials in terms of a tridiagonal determinant and, as applications of the newly-established closed formula for the Horadam polynomials, derive closed formulas for the generalized Fibonacci polynomials, the Lucas polynomials, the Pell-Lucas polynomials, and the Chebyshev polynomials of the first kind in terms of tridiagonal determinants. © 2019 by the authors

On the (p, q)-Chebyshev polynomials and related polynomials

In this paper, we introduce (p, q)-Chebyshev polynomials of the first and second kind that reduces the (p, q)-Fibonacci and the (p, q)-Lucas polynomials. These polynomials have explicit forms and generating functions are given. Then, derivative properties between these first and second kind polynomials, determinant representations, multilateral and multilinear generating functions are derived. © 2019 by the authors

On the (p, q)-Chebyshev polynomials and related polynomials

In this paper, we introduce ( p , q ) ⁻Chebyshev polynomials of the first and second kind that reduces the ( p , q ) ⁻Fibonacci and the ( p , q ) ⁻Lucas polynomials. These polynomials have explicit forms and generating functions are given. Then, derivative properties between these first and second kind polynomials, determinant representations, multilateral and multilinear generating functions are derived

New families of three-variable polynomials coupled with well-known polynomials and numbers

In this paper, firstly the definitions of the families of three-variable polynomials with the new generalized polynomials related to the generating functions of the famous polynomials and numbers in literature are given. Then, the explicit representation and partial differential equations for new polynomials are derived. The special cases of our polynomials are given in tables. In the last section, the interesting applications of these polynomials are found. © 2019 by the authors