Fibonacci-Like Polynomials and Some Properties
-
https://doi.org/10.14419/ijams.v1i3.900
-
Fibonacci polynomials, Fibonacci-Like polynomials, Binet’s formula. -
Abstract
The Fibonacci and generalized Fibonacci polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, we introduce Fibonacci-Like polynomials (FLP) and describe some properties. We obtain few properties by defined Fibonacci-Like polynomials - matrix. Further we establish few identities like Catalan’s, Cassini’s, d’Ocagne’s through Binet’s formula and few identities by using explicit summation formula which are related to hypergeometric functions of FLP.
-
References
- Demiriturk, B., Fibonacci and Lucas Sums by Matrix Methods, Int. Math. Forum, Vol. 5, No. 3 (2010), 99-107.
- Garth, D., Mills, D., Mitchell, P., Polynomials Generated by the Fibonacci Sequence, Journal of Integer Sequences, Vol. 10 (2007), Article 07.6.8.
- Horadam, A. F., Mahon, J. M., Pell and Pell-Lucas Polynomials, Fibonacci Quart., Vol. 23, No. 1 (1985), 7-20.
- Horzum, T., Kocer, E. G., On Some Properties of Horadam Polynomials, Int. Math. Forum, Vol. 4, No. 25 (2009), 1243-1252.
- Koken, F., Bozkurt, D., On the Jacobsthal Numbers by Matrix Methods, Int. J. Contemp. Math. Sciences, Vol. 3, No. 13 (2008), 605-614.
- Koken, F., Bozkurt, D., On the Jacobsthal Numbers by Matrix Methods, Int. J. Contemp. Math. Sciences, Vol. 3, No. 33 (2008), 1629-1633.
- Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley and Sons. New York, 2001.
- Lupas, A., A Guide of Fibonacci and Lucas Polynomial, Octagon Mathematics Magazine, Vol. 7, No.1 (1999), 2-12.
- Silvester, J. R., Fibonacci Properties by Matrix Methods, Mathematical Gazette, 63 (1979), 188- 191.
- Singh, B., Sikhwal, O., Bhatnagar, S., Fibonacci-Like Sequence and its Properties, Int. J. Contemp. Math. Sciences, Vol. 5, No. 18 (2010), 859-868.
-
Downloads
-
How to Cite
Bhatnagar, S., Singh, B., & Sikhwal, O. (2013). Fibonacci-Like Polynomials and Some Properties. International Journal of Advanced Mathematical Sciences, 1(3), 152-157. https://doi.org/10.14419/ijams.v1i3.900
