Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2016, Cilt: 29 Sayı: 1, 109 - 113, 21.03.2016

Emine Gokcen Kocer , Serife Tuncez

Öz

Kaynakça

  • 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

Yıl 2016, Cilt: 29 Sayı: 1, 109 - 113, 21.03.2016

Emine Gokcen Kocer , Serife Tuncez

Öz

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.

Anahtar Kelimeler

Bivariate fibonacci Polynomial Binet Formula polynomials

Kaynakça

  • 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).
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Mathematics
Yazarlar

Emine Gokcen Kocer

Serife Tuncez

Yayımlanma Tarihi 21 Mart 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 29 Sayı: 1

Kaynak Göster

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. Mart 2016;29(1):109-113.
Chicago Kocer, Emine Gokcen, ve Serife Tuncez. “Bivariate Fibonacci and Lucas Like Polynomials”. Gazi University Journal of Science 29, sy. 1 (Mart 2016): 109-13.
EndNote Kocer EG, Tuncez S (01 Mart 2016) Bivariate Fibonacci and Lucas Like Polynomials. Gazi University Journal of Science 29 1 109–113.
IEEE E. G. Kocer ve S. Tuncez, “Bivariate Fibonacci and Lucas Like Polynomials”, Gazi University Journal of Science, c. 29, sy. 1, ss. 109–113, 2016.
ISNAD Kocer, Emine Gokcen - Tuncez, Serife. “Bivariate Fibonacci and Lucas Like Polynomials”. Gazi University Journal of Science 29/1 (Mart 2016), 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 ve Serife Tuncez. “Bivariate Fibonacci and Lucas Like Polynomials”. Gazi University Journal of Science, c. 29, sy. 1, 2016, ss. 109-13.
Vancouver Kocer EG, Tuncez S. Bivariate Fibonacci and Lucas Like Polynomials. Gazi University Journal of Science. 2016;29(1):109-13.