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Generalized Fibonacci Polynomials and some Identities

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
Authors:
G. P. S. Rathore, Omprakash Sikhwal, Ritu Choudhary
10.5120/ijca2016911990

G P S Rathore, Omprakash Sikhwal and Ritu Choudhary. Generalized Fibonacci Polynomials and some Identities. International Journal of Computer Applications 153(12):4-8, November 2016. BibTeX

@article{10.5120/ijca2016911990,
	author = {G. P. S. Rathore and Omprakash Sikhwal and Ritu Choudhary},
	title = {Generalized Fibonacci Polynomials and some Identities},
	journal = {International Journal of Computer Applications},
	issue_date = {November 2016},
	volume = {153},
	number = {12},
	month = {Nov},
	year = {2016},
	issn = {0975-8887},
	pages = {4-8},
	numpages = {5},
	url = {http://www.ijcaonline.org/archives/volume153/number12/26539-2016911990},
	doi = {10.5120/ijca2016911990},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. Generalization of Fibonacci polynomial has been done using various approaches. One usually found in the literature that the generalization is done by varying the initial conditions. In this paper, Generalized Fibonacci polynomials are defined by Wn(X)=XWn-1(X)+Wn-2(X); n≥2 with W0(X)=2b and W1(X) = a+b, where a and b are integers. Further, some basic identities are generated and derived by generating function.

References

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Keywords

Fibonacci polynomial, Lucas polynomial, Generalized Fibonacci polynomial, Generating function