Generalized Fibonacci-Lucas Polynomials

Authors

  • Mamta Singh

    School of Studies in Mathematics, Vikram University Ujjain
  • Omprakash Sikhwal

    Department of Mathematics, Mandsaur Institute of Technology Mandsaur (M. P.)
  • Vibhoj Parsai

  • Yogesh Gupta

    School of Studies in Mathematics,Vikram university,Ujjain

How to Cite

Singh, M., Sikhwal, O., Parsai, V., & Gupta, Y. (2014). Generalized Fibonacci-Lucas Polynomials. International Journal of Advanced Mathematical Sciences, 2(1), 81-87. https://doi.org/10.14419/ijams.v2i1.1388

DOI:

https://doi.org/10.14419/ijams.v2i1.1388

Abstract

Various sequences of polynomials by the names of Fibonacci and Lucas polynomials occur in the literature over a century. The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, Generalized Fibonacci-Lucas Polynomials are introduced and defined by the recurrence relation with and . Some basic identities of Generalized Fibonacci-Lucas Polynomials are obtained by method of generating function.

 

Keywords: Fibonacci polynomials, Lucas polynomials, Generalized Fibonacci polynomials, Generalized Fibonacci-Lucas polynomials.

 

References

  1. Basin, S. L., The appearance of Fibonacci Numbers and the Q Matrix in Electrical Network Theory, Mathematics Magazine, Vol. 36, No. 2, (1963), 84-97.
  2. Bicknell, Marjorie. A Primer for the Fibonacci Numbers: part VII - An introduction to Fibonacci Polynomials and 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), 268-172.
  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 and Pell-Lucas Polynomials, Fibonacci Quart., Vol. 23, No. 1 (1985), 7-20.
  9. Koshy, T., Fibonacci and Lucas numbers with Applications, John Wiley and Sons. New York, 2001.
  10. Lupas, A., A Guide of Fibonacci and Lucas Polynomial, Octagon Mathematics Magazine, Vol. 7, No.1 (1999), 2-12.
  11. Singh, B., Bhatnagar,S. and Sikhwal, O., Fibonacci-Like Polynomials and Some Properties, International Journal of Advanced Mathematical Sciences, 1 (3) (2013), 152-157.
  12. Singh, B., Sikhwal, O. and Panwar, Y. K., Generalized Determinantal Identities Involving Lucas Polynomials, Applied Mathematical Sciences, Vol. 3 (2009), No. 8, 377-388.
  13. Swamy, M. N. S., Generalized Fibonacci and Lucas Polynomials and their associated diagonal polynomials, The Fibonacci Quarterly Vol. 37, (1999), 213-222.
  14. Webb, W. A. and Parberry, E. A., Divisibility Properties of Fibonacci Polynomials, The Fibonacci Quarterly Vol. 7, No. 5 (1969), 457-463.

Downloads

Additional Files

How to Cite

Singh, M., Sikhwal, O., Parsai, V., & Gupta, Y. (2014). Generalized Fibonacci-Lucas Polynomials. International Journal of Advanced Mathematical Sciences, 2(1), 81-87. https://doi.org/10.14419/ijams.v2i1.1388