A Closed Formula for the Horadam Polynomials in Terms of a Tridiagonal Determinant

Symmetry

Can Kızılateş¹  Wei-Shih Du²  Feng Qi³ 

[1] Department of Mathematics, Faculty of Arts and Sciences, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey;Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan;Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, China;

关键词: closed formula;    Horadam polynomial, tridiagonal determinant;    generalized Fibonacci polynomial;    Lucas polynomial;    Pell–Lucas polynomial;    Chebyshev polynomial of the first kind;    Chebyshev polynomial of the second kind;   

DOI  :  10.3390/sym11060782

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown