Fibonacci-Like Polynomials and Some Properties

Authors

  • Shikha Bhatnagar
  • Bijendra Singh
  • Omprakash Sikhwal

DOI:

https://doi.org/10.14419/ijams.v1i3.900

Published

29-06-2013

Keywords:

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.

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

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