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Izvestiya: Mathematics, 2018, Volume 82, Issue 6, Pages 1265–1277
DOI: https://doi.org/10.1070/IM8676 (Mi im8676) 		 
Trigonometric factorizations of the Horadam sequence and its companion sequence

Z. Siar

Bingöl University, Faculty of Arts and Sciences, Department of Mathematics, Turkey
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DOI: https://doi.org/10.1070/IM8676
Abstract: We consider the Horadam sequence $\{W_n\}$ and its companion sequence $\{X_n\}$ satisfying a second-order recurrence. We generalize earlier results by giving new results about factorizations of these sequences. In order to obtain these results, we use connections between the determinants of tridiagonal matrices and the terms of these sequences, and also take advantage of Chebyshev polynomials of the second kind.
Keywords: Horadam sequence, determinant, tridiagonal matrix, eigenvalue.
Received: 22.03.2017
Revised: 27.03.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2018, Volume 82, Issue 6, Pages 200–212
DOI: https://doi.org/10.4213/im8676
Bibliographic databases:
Document Type: Article
UDC: 512.643+517.962.27
MSC: 11B39, 11C20, 15B05, 15A18
Language: English
Original paper language: Russian
Citation: Z. Siar, “Trigonometric factorizations of the Horadam sequence and its companion sequence”, Izv. RAN. Ser. Mat., 82:6 (2018), 200–212; Izv. Math., 82:6 (2018), 1265–1277
Citation in format AMSBIB
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:254
    Russian version PDF:40
    English version PDF:10
    References:40
    First page:17
     
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