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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 5 | Year 2019 | Article Id. IJMTT-V65I5P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I5P512

Generalized Identities on Derivatives of p(y) - Fibonacci Polynomial And p(y)-Lucas Polynomial


Vipin Verma, Tahseen Ahmed Itoo
Abstract

The Fibonacci and Lucas Polynomials are well known for having interesting and amazing properties and identities. In this paper we introduce p(y)-Fibonacci and p(y)-Lucas polynomials where p(y) is a polynomial with real coefficients and some basic identities are derived by using generating function of these polynomials.

Keywords
p(y)-Fibonacci polynomial, p(y)-Lucas polynomial.
References

[1] Bicknell Marjorie, A Primer for the Fibonacci Number: part and VII – An introduction to Fibonacci polynomials their Divisibility properties, The Fibonacci Quarterly, Vol. 8, No.4 (1970), 407-420.
[2] Doman B. G. S. and Williams, J. K., Fibonacci and Lucas Polynomials, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 90, Issue 3 (1981), 385-387.
[3] Falcon S, Plaza A, On k-Fibonacci sequences and polynomials and their derivatives. Chaos, Solitons & Fractals, 39(2009),1005-19.
[4] Hoggatt V.E. Jr, The Fibonacci and Lucas Numbers, Boston, M A: Houghton Mifflin, 1969.
[5] Nalli A, Haukkanen P, On generalized Fibonacci and Lucas polynomials. Chaos Solitons Fractals, 42(2009), 3179-3186.
[6] Sikhwal Omprakash, Generalized Fibonacci Polynomials and some identities International Journal of Computer Applications, Volume 153(12) (2016), 4-8.

Citation :

Vipin Verma, Tahseen Ahmed Itoo, "Generalized Identities on Derivatives of p(y) - Fibonacci Polynomial And p(y)-Lucas Polynomial," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 5, pp. 86-89, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I5P512

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