Complex Factorizations of the Lucas Sequences via Matrix Methods | Zendy

Honglin Wu | Zendy

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Complex Factorizations of the Lucas Sequences via Matrix Methods

Author(s) -

Honglin Wu

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/387675

Subject(s) - tridiagonal matrix , lucas sequence , sequence (biology) , lucas number , mathematics , chebyshev polynomials , chebyshev filter , connection (principal bundle) , matrix (chemical analysis) , chebyshev nodes , algebra over a field , fibonacci polynomials , pure mathematics , discrete mathematics , classical orthogonal polynomials , orthogonal polynomials , fibonacci number , mathematical analysis , eigenvalues and eigenvectors , physics , geometry , materials science , quantum mechanics , biology , composite material , genetics

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

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