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Complex Factorizations of the Lucas Sequences via Matrix Methods

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  • Honglin Wu

Abstract

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.

Suggested Citation

  • Honglin Wu, 2014. "Complex Factorizations of the Lucas Sequences via Matrix Methods," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, January.
    • Handle: RePEc:hin:jnljam:387675
    DOI: 10.1155/2014/387675
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