Document Zbl 1406.11016

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Complex factorizations of the Lucas sequences via matrix methods. (English) Zbl 1406.11016

J. Appl. Math. 2014, Article ID 387675, 6 p. (2014).

Summary: Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev polynomials of the second kind. Furthermore, we also obtain the complex factorizations of the second Lucas sequence by the similar matrix method using Chebyshev polynomials of the first kind.

Cited in 1 Document

MSC:

11B39

Fibonacci and Lucas numbers and polynomials and generalizations

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