Research Article
BibTex RIS Cite

Year 2016, Volume: 29 Issue: 1, 109 - 113, 21.03.2016

Emine Gokcen Kocer , Serife Tuncez

Abstract

References

  • Belbachir, H., Bencherif, F., “On Some Properties of Bivariate Fibonacci and Lucas Polynomials”, Journal of Integer Sequences ,11, Article 08.2.6, (2008).
  • Catalani, M., “Some Formulae for Bivariate Fibonacci and Lucas Polynomials”, Arxiv: math.CO/0406323v1, (2004).
  • Catalani, M., “Generalized Bivariate Fibonacci Polynomials”, Arxiv: math/0211366v2, (2004).
  • Djordjevic, GB., “Some properties of a class of polynomials”, Matematiqki Vesnik, 49: 265-271 (1997).
  • Djordjevic, GB., “Some properties of partial derivatives of Generalized Fibonacci and Lucas polynomials”, The Fibonacci Quarterly, 39: 138-141 (2001).
  • Frei, G., “Binary Lucas and Fibonacci polynomials”, Mathematische Nachrichten, 96: 83-112 (1980).
  • Koshy T., Fibonacci and Lucas Numbers with Applications, A.Wiley- Interscience Publication, (2001).
  • MacHenry, T., “A Subgroupof units in the ring of arithmetic functions”, Rocky Mountain Journal of Mathematics, 29:1055-1064, (1999).
  • MacHenry, T., “Generalized Fibonacci and Lucas Polynomials and Multiplicative Arithmetic Functions”, The Fibonacci Quarterly, 38:167-173, (2000).
  • MacHenry, T., Geanina, T., “Reflections on symmetric polynomials and arithmetic functions”, Rocky Mountain Journal of Mathematics, 35:901-928, (2005).
  • Nalli, A., Haukkanen, P., “On Generalizing Fibonacci and Lucas Polynomials”, Chaos, Solitions and Fractals 42: 3179-3186, (2009).
  • Swamy, M.N.S., “Network properties of a pair of generalized polynomials”, proceedings of the 1998 Midwest Symposium on systems and circuits.
  • Tan, M., Zhang, Y. A., “Note on bivariate and trivariate Fibonacci polynomials”, Southeast Asian Bulletin of Math., 29: 975-990, (2005).
  • Tuglu, N., Kocer, E.G., Stakhov, A., “Bivariate Fibonacci Like -Polynomials”, Applied Mathematics and Computation, 217: 10239-10246, (2011).

Bivariate Fibonacci and Lucas Like Polynomials

Year 2016, Volume: 29 Issue: 1, 109 - 113, 21.03.2016

Emine Gokcen Kocer , Serife Tuncez

Abstract

In this article, we study the generalized bivariate Fibonacci (GBF) and generalized bivariate Lucas (GBL) polynomials from specifying p(x,y) and q(x,y)  , classical bivariate Fibonacci and Lucas polynomials (  p(x,y)=x and q(x,y)=y ). Afterwards, we obtain the some properties of the GBF and GBL polynomials.

Keywords

Bivariate fibonacci Polynomial Binet Formula polynomials

References

  • Belbachir, H., Bencherif, F., “On Some Properties of Bivariate Fibonacci and Lucas Polynomials”, Journal of Integer Sequences ,11, Article 08.2.6, (2008).
  • Catalani, M., “Some Formulae for Bivariate Fibonacci and Lucas Polynomials”, Arxiv: math.CO/0406323v1, (2004).
  • Catalani, M., “Generalized Bivariate Fibonacci Polynomials”, Arxiv: math/0211366v2, (2004).
  • Djordjevic, GB., “Some properties of a class of polynomials”, Matematiqki Vesnik, 49: 265-271 (1997).
  • Djordjevic, GB., “Some properties of partial derivatives of Generalized Fibonacci and Lucas polynomials”, The Fibonacci Quarterly, 39: 138-141 (2001).
  • Frei, G., “Binary Lucas and Fibonacci polynomials”, Mathematische Nachrichten, 96: 83-112 (1980).
  • Koshy T., Fibonacci and Lucas Numbers with Applications, A.Wiley- Interscience Publication, (2001).
  • MacHenry, T., “A Subgroupof units in the ring of arithmetic functions”, Rocky Mountain Journal of Mathematics, 29:1055-1064, (1999).
  • MacHenry, T., “Generalized Fibonacci and Lucas Polynomials and Multiplicative Arithmetic Functions”, The Fibonacci Quarterly, 38:167-173, (2000).
  • MacHenry, T., Geanina, T., “Reflections on symmetric polynomials and arithmetic functions”, Rocky Mountain Journal of Mathematics, 35:901-928, (2005).
  • Nalli, A., Haukkanen, P., “On Generalizing Fibonacci and Lucas Polynomials”, Chaos, Solitions and Fractals 42: 3179-3186, (2009).
  • Swamy, M.N.S., “Network properties of a pair of generalized polynomials”, proceedings of the 1998 Midwest Symposium on systems and circuits.
  • Tan, M., Zhang, Y. A., “Note on bivariate and trivariate Fibonacci polynomials”, Southeast Asian Bulletin of Math., 29: 975-990, (2005).
  • Tuglu, N., Kocer, E.G., Stakhov, A., “Bivariate Fibonacci Like -Polynomials”, Applied Mathematics and Computation, 217: 10239-10246, (2011).
There are 14 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Emine Gokcen Kocer

Serife Tuncez This is me

Publication Date March 21, 2016
Published in Issue Year 2016 Volume: 29 Issue: 1

Cite

APA Kocer, E. G., & Tuncez, S. (2016). Bivariate Fibonacci and Lucas Like Polynomials. Gazi University Journal of Science, 29(1), 109-113.
AMA Kocer EG, Tuncez S. Bivariate Fibonacci and Lucas Like Polynomials. Gazi University Journal of Science. March 2016;29(1):109-113.
Chicago Kocer, Emine Gokcen, and Serife Tuncez. “Bivariate Fibonacci and Lucas Like Polynomials”. Gazi University Journal of Science 29, no. 1 (March 2016): 109-13.
EndNote Kocer EG, Tuncez S (March 1, 2016) Bivariate Fibonacci and Lucas Like Polynomials. Gazi University Journal of Science 29 1 109–113.
IEEE E. G. Kocer and S. Tuncez, “Bivariate Fibonacci and Lucas Like Polynomials”, Gazi University Journal of Science, vol. 29, no. 1, pp. 109–113, 2016.
ISNAD Kocer, Emine Gokcen - Tuncez, Serife. “Bivariate Fibonacci and Lucas Like Polynomials”. Gazi University Journal of Science 29/1 (March2016), 109-113.
JAMA Kocer EG, Tuncez S. Bivariate Fibonacci and Lucas Like Polynomials. Gazi University Journal of Science. 2016;29:109–113.
MLA Kocer, Emine Gokcen and Serife Tuncez. “Bivariate Fibonacci and Lucas Like Polynomials”. Gazi University Journal of Science, vol. 29, no. 1, 2016, pp. 109-13.
Vancouver Kocer EG, Tuncez S. Bivariate Fibonacci and Lucas Like Polynomials. Gazi University Journal of Science. 2016;29(1):109-13.