On the (s,t)-Pell and (s,t)-Pell-Lucas Polynomials
Main Article Content
Abstract
In this paper, we introduced the generalization of Pell and Pell-Lucas polynomials, which are called -Pell and - Pell-Lucas polynomials. We also give the Binet formula and the generating function for these polynomials. Finally, we obtain some identities by using the Binet formulas.
Article Details
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Koshy T. Pell and Pell-Lucas Numbers with Applications. Berlin: Springer; 2014.
Koshy T. Fibonacci and Lucas Numbers with Applications. New York: John Wiley and Sons Inc; 2001.
Naschie M.S. El. The Fibonacci Code Behind Super Strings and P-Branes: An Answer to M. Kaku's Fundamental Question. Chaos, Solitons & Fractals. 2007; 31: 537–547.
Naschie M.S. El. Notes on Superstrings and the Infinite Sums of Fibonacci and Lucas Numbers. Chaos, Solitons & Fractals. 2001; 12: 1937–1940.
Stakhov A.P. Fibonacci Matrices: A Generalization of the "Cassini Formula" and a New Coding Theory. Chaos, Solitons Fractals. 2006; 30: 56–66.
Stakhov A.P. The Generalized Principle of the Golden Section and Its Applications in Mathematics, Science and Engineering. Chaos, Solitons & Fractals. 2005; 26: 263–289.
Gulec H.H, Taskara N. On the (s,t)-Pell and (s,t)-Pell Lucas sequences and their matrix representations. Applied Mathematics Letters. 2012; 25: 1554–1559.
Srisawat S, Sriprad W. On the (s,t)-Pell and (s,t)-Pell-Lucas numbers by matrix methods. Annales Mathematicae et Informaticae. 2016; 46: 195-204.
Srisawat S, Sriprad W. Some identities for (s,t)-Pell and (s,t)-Pell-Lucas numbers and its application to Diophantine equations. SNRU Journal of Science and Technology. 2017; 9(1): 424-431.
Srisawat S, Sriprad W. On Some Identities and Generating Functions for (s,t)-Pell and (s,t)-Pell-Lucas Numbers. Science and Technology RMUTT Journal. 2017; 7(2): 194–199.
Hogatt V. E. Fibonacci and Lucas numbers. Borton: Houshton Mifflin Company, 1965.
Horadam A. F., Mahon B. J. M. Pell and Pell-Lucas polynomials. Fibonacci Quart. 1985; 23:7-20.
CATARINO P. Diagonal function of the k-Pell and k-Pell-Lucus polynomials and some identities. In: Acta Math. Univ. Comenianae. 2018; 87: 147–159.
Sergio F. Angle Plazza. On k-Fibonacci sequences and polynomials and their derivatives. In: Chaos and Solitons and Fractals. 2009; 39: 1005–1019.