CFP last date
22 April 2024
Call for Paper
May Edition
IJCA solicits high quality original research papers for the upcoming May edition of the journal. The last date of research paper submission is 22 April 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Generalized Fibonacci Polynomials and some Identities

by G. P. S. Rathore, Omprakash Sikhwal, Ritu Choudhary
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 153 - Number 12
Year of Publication: 2016
Authors: G. P. S. Rathore, Omprakash Sikhwal, Ritu Choudhary
10.5120/ijca2016911990

G. P. S. Rathore, Omprakash Sikhwal, Ritu Choudhary . Generalized Fibonacci Polynomials and some Identities. International Journal of Computer Applications. 153, 12 ( Nov 2016), 4-8. DOI=10.5120/ijca2016911990

@article{ 10.5120/ijca2016911990,
author = { G. P. S. Rathore, Omprakash Sikhwal, Ritu Choudhary },
title = { Generalized Fibonacci Polynomials and some Identities },
journal = { International Journal of Computer Applications },
issue_date = { Nov 2016 },
volume = { 153 },
number = { 12 },
month = { Nov },
year = { 2016 },
issn = { 0975-8887 },
pages = { 4-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume153/number12/26539-2016911990/ },
doi = { 10.5120/ijca2016911990 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:58:55.866949+05:30
%A G. P. S. Rathore
%A Omprakash Sikhwal
%A Ritu Choudhary
%T Generalized Fibonacci Polynomials and some Identities
%J International Journal of Computer Applications
%@ 0975-8887
%V 153
%N 12
%P 4-8
%D 2016
%I Foundation of Computer Science (FCS), NY, 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
  1. Basin, S. L., The appearance of Fibonacci numbers and the Q Matrix in Electrical Network Theory Magazine, Vol. 36, No. 2, (1963) 84-90.
  2. Bicknell, Marjorie. A Primer for the Fibonacci Number: part and 7th – An introduction to Fibonacci polynomials their Divisibility properties, The Fibonacci Quarterly, Vol. 8, No.4 (1970), 407-420.
  3. Doman, B. G. S. and Williams ,J. K.., Fibonacci and Lucas Polynomials, Mathematical Proceedings of the Cambridge Philosophical Society, 90,Part 3 (1981), 385-387.
  4. Glasson, Alan R., Remainder Formulas, Involving Generalized Fibonacci and Lucas Polynomials, The Fibonacci Quarterly, vol. 33, No. 3,(1995),36-39.
  5. Hayes, Richard A., Fibonacci and Lucas polynomials, Master’s Thesis, San Jose State college, January, (1965), 36-39.
  6. Hoggatt, V. E. Jr., Private communication of Nov. 17, 1965 to Selmo Tauber , The Fibonacci Quarterly, Vol. 6, (1968), 99.
  7. Hoggatt, V. E. Jr. and Long, C. T., Divisibility properties of Fibonacci Polynomials, The Fibonacci Quarterly, Vol. 12, No. 2, (1974),113-120.
  8. Horadam, A. F., Mahon, J. M., Pell-Lucas Polynomials, The Fibonacci Quarterly, Vol. 23,No. 1 (1985),7-20.
  9. Koshy, T., Fibonacci and Lucas Number with application, John Wiley and Sons. New York, 2001.
  10. Lupas A., A Guide of Fibonacci and Lucas Polynomials, Octagon Mathematics Magazine, Vol. 7, No. 1 (1999), 2-12.
  11. Singh B., Bhatnagar S., Sikhwal O., Fibonacci-Like Polynomials and Identities, International Journal of Advanced Mathematical Sciences, 1 (3) (2013), 152-157.
  12. Singh M., Sikhwal O., and Gupta Y., Generalized Fibonacci-Lucas Polynomials, International Journal of Advanced Mathematical Sciences ,2(1)(2014), 81-87.
  13. Singh B., Sikhwal O., Bhatnagar S., Fibonacci-Like Sequence and its Properties, Int. J. Contemp. Math. Sciences, Vol. 5,No. 18, (2010), 859-868.
  14. Singh B., Sikhwal O., and Panwar Y. K., Determinantal Identities Involving Lucas Polynomials, Applied Mathematical Sciences Vol. 3, (2009), No. 8, 377-388.
Index Terms

Computer Science
Information Sciences

Keywords

Fibonacci polynomial Lucas polynomial Generalized Fibonacci polynomial Generating function

Powered by PhDFocusTM