Geodesic
Positive Integer Powers of One Type of Complex Tridiagonal Matrix
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4
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In this paper, we firstly present a general expression for the entries of the $r${th }($r\in\mathbb{N}$) power of a certain $n$-square complex tridiagonal matrix, in terms of the Chebyshev polynomials of the first kind. Secondly, we obtain two complex factorizations for Fibonacci and Pell numbers. We also give some Maple 13 procedures in order to verify our calculations.
Classification : 47B36, 15A18, 65F15, 11B39 
@article{BMMS_2014_37_4_a5,
     author = {Ahmet \"Otele\c{s} and Mehmet Akbulak},
     title = {Positive {Integer} {Powers} of {One} {Type} of {Complex} {Tridiagonal} {Matrix}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a5/}
}
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IS  - 4
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%A Mehmet Akbulak
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Ahmet Öteleş; Mehmet Akbulak. Positive Integer Powers of One Type of Complex Tridiagonal Matrix. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a5/