The Exponential Representations of Pell and Its Generalized Matrix Sequences
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In this paper we define a matrix sequence called the Pell matrix sequence whose elements consist of Pell numbers. Using a positive parameter k, we generalize the Pell matrix sequence to a k-Pell matrix sequence and using two parameters s, t we generalize them to (s, t)-Pell matrix sequences. We give the basic properties of these matrix sequences. Then, using these properties we obtain exponential representations of the Pell matrix sequence and its generalizations in different ways.
Abstract
In this paper we define a matrix sequence called the Pell matrix sequence whose elements consist of Pell numbers. Using a positive parameter k, we generalize the Pell matrix sequence to a k-Pell matrix sequence and using two parameters s, t we generalize them to (s, t)-Pell matrix sequences. We give the basic properties of these matrix sequences. Then, using these properties we obtain exponential representations of the Pell matrix sequence and its generalizations in different ways.
참고문헌 (6)
- A. F. Horadam, "Pell Identities", Fibonacci Quart., 9(3), pp.245~252 (1971)
- H. H. Gulec, "On the (s, t)-Pell and (s, t)-Pell–Lucas sequences and their matrix representations", Appl. Math. Lett., 25(10), pp.1554~1559 (2012)
- P. Catarino, "On Some Identities and Generating Functions for k-Pell Numbers", Int. J. Math. Anal., 7(38), pp.1877~1884 (2013)
- S. Srisawat, "On the (s, t)-Pell and Pell-Lucas Numbers by Matrix Methods", Ann. Math. Inform., 46, pp.195~204 (2016)
- S. Uygun, "The Exponential Representations of Jacobsthal Matrix Sequences", J. Math. Anal., 7(5), pp.140~146 (2016)
- T. Koshy, "Pell and Pell-Lucas Numbers with Applications" (2014), Springer