Korean J. Math.  Vol 23, No 3 (2015)  pp.371-377
DOI: https://doi.org/10.11568/kjm.2015.23.3.371

Complex factorizations of the generalized Fibonacci sequences $\{q_n\}$

Sang Pyo Jun

Abstract


In this note, we consider a generalized Fibonacci sequence $\{q_n\}$. Then give a connection between the sequence $\{q_n\}$ and the Chebyshev polynomials of the second kind $U_n(x)$. With the aid of factorization of Chebyshev polynomials of the second kind $U_n(x)$, we derive the complex factorizations of the sequence $\{q_n\}$.

Keywords


generalized Fibonacci sequences, tridiagonal matrices, Chebyshev polynomials, complex factorization.

Subject classification

11B39.

Sponsor(s)

Funding for this paper was provided by Namseoul University.

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