Generalized Fibonacci-Like Polynomials and Some Identities

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, Generalized Fibonacci-Lucas Polynomials is introduced and defined by with and. some basic identities established and derived by standard methods.

    Keywords: Fibonacci Polynomials, Lucas Polynomials, Generalized Fibonacci Polynomials

    MSC: 2000: 11B37, 11B39


  • 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. http://dx.doi.org/10.2307/2688890.
      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. http://dx.doi.org/10.1017/S0305004100058850.
      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. http://dx.doi.org/10.1002/9781118033067.
      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, 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.
      15. Swamy, M. N. S., Generalized Fibonacci and Lucas Polynomials and their associated diagonal polynomials, The Fibonacci Quarterly Vol. 37, (1999), 213-222.
      16. Webb, W. A. and Parberry, E. A., Divisibility Properties of Fibonacci Polynomials, The Fibonacci Quarterly Vol. 7, No. 5 (1969), 457-463.

 

View

Download

Article ID: 3126
 
DOI: 10.14419/gjma.v2i4.3126




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.