Trigonometric Factorizations of the Pell and Jacobsthal Sequences
Abstract
The Pell and Jacobsthal numbers have inspired many studies in mathematics, especially in number theory. In this paper, we derive the trigonometric factorizations of the Pell and Jacobsthal sequences by using determinants of two specific new tridiagonal matrices and the roots of the Chebyshev polynomial of the second kind. Furthermore, we provide two Maple procedures to calculate the trigonometric factorizations of these integer sequences.
Keywords
Pell sequences, Jacobsthal sequences, factorizations, tridiagonal matrices, determinants
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