The Pell and Pell-Lucas Numbers via Square Roots of Matrices - Arslan, Saadet; Köken, Fikri (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.