The Pell and Pell-Lucas Numbers via Square Roots of Matrices (Journal of Informatics and Mathematical Sciences, 2016)
In this paper, the Pell and Pell-Lucas numbers with specialized rational subscripts are derived from general expressions by square roots of the matrices \(M^n\) and \(N^n\). Besides, we reveal that the identities involving these numbers are produced by square roots of matrices \(M^{n/2}\) and \(N^{n/2}\). Further we show that the matrices \(M^n\) and \(N^n\) are generalized to rational powers by using the Abel's functional equation.
Keywords: Pell and Pell-Lucas Numbers; Square Roots of Matrices