Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 4 Sayı: 2, 90 - 99, 31.12.2023

Yashwant Panwar

https://doi.org/10.54559/jauist.1395447

Öz

Kaynakça

  • M. Catalani, Some formulae for bivariate Fibonacci and Lucas polynomials (2004) 9 pages, https://arxiv.org/abs/math/0406323.
  • M. Catalani, Identities for Fibonacci and Lucas polynomials derived from a book of Gould (2004) 7 pages, https://arxiv.org/abs/math/0407105.
  • M. Catalani, Generalized bivariate Fibonacci polynomials (2004) 11 pages, https://arxiv.org/abs/math/0211366.
  • H. Belbachir, F. Bencherif, On some properties of bivariate Fibonacci and Lucas polynomials, Journal of Integer Sequences 11 (2) (2008) 08.2.6 10 pages.
  • N. Tuğlu, E. G. Koçer, A. Stakhov, Bivariate Fibonacci like p-polynomials, Applied Mathematics and Computation 217 (24) (2011) 10239–10246.
  • S. Halıcı, Z. Akyüz, On sum formulae for bivariate Pell polynomials, Far East Journal of Applied Mathematics 41 (2) (2010) 101–110.
  • N. Saba, A. Boussayoud, Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials, Open Journal of Mathematical Sciences 4 (1) (2020) 179–185.
  • T. Machenry, A subgroup of the group of units in the ring of arithmetic functions, Rocky Mountain Journal of Mathematics 29 (3) (1999) 1055–1065.
  • T. Machenry, Generalized Fibonacci and Lucas polynomials and multiplicative arithmetic functions, Fibonacci Quarterly 38 (2) (2000) 167–173.
  • T. Machenry, G. Tudose, Reflections on symmetric polynomials and arithmetic functions, Rocky Mountain Journal of Mathematics 35 (3) (2006) 901–928.
  • T. Machenry, K. Wong, Degree k linear recursions mod(p) and number fields, Rocky Mountain Journal of Mathematics 41 (4) (2011) 1303–1327.

Some identities of bivariate Pell and bivariate Pell-Lucas polynomials

Yıl 2023, Cilt: 4 Sayı: 2, 90 - 99, 31.12.2023

Yashwant Panwar

https://doi.org/10.54559/jauist.1395447

Öz

In this paper, we obtain some identities for the bivariate Pell polynomials and bivariate Pell-Lucas polynomials. We establish some sums and connection formulas involving them. Moreover, we present its two cross two matrices representation and find some of its properties, such as the b^th power of the matrix. We finally derive the identities by using Binet’s formula, generating function, and induction method.

Anahtar Kelimeler

Bivariate Pell polynomials bivariate Pell-Lucas polynomials Binet’s formula generating function

Kaynakça

  • M. Catalani, Some formulae for bivariate Fibonacci and Lucas polynomials (2004) 9 pages, https://arxiv.org/abs/math/0406323.
  • M. Catalani, Identities for Fibonacci and Lucas polynomials derived from a book of Gould (2004) 7 pages, https://arxiv.org/abs/math/0407105.
  • M. Catalani, Generalized bivariate Fibonacci polynomials (2004) 11 pages, https://arxiv.org/abs/math/0211366.
  • H. Belbachir, F. Bencherif, On some properties of bivariate Fibonacci and Lucas polynomials, Journal of Integer Sequences 11 (2) (2008) 08.2.6 10 pages.
  • N. Tuğlu, E. G. Koçer, A. Stakhov, Bivariate Fibonacci like p-polynomials, Applied Mathematics and Computation 217 (24) (2011) 10239–10246.
  • S. Halıcı, Z. Akyüz, On sum formulae for bivariate Pell polynomials, Far East Journal of Applied Mathematics 41 (2) (2010) 101–110.
  • N. Saba, A. Boussayoud, Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials, Open Journal of Mathematical Sciences 4 (1) (2020) 179–185.
  • T. Machenry, A subgroup of the group of units in the ring of arithmetic functions, Rocky Mountain Journal of Mathematics 29 (3) (1999) 1055–1065.
  • T. Machenry, Generalized Fibonacci and Lucas polynomials and multiplicative arithmetic functions, Fibonacci Quarterly 38 (2) (2000) 167–173.
  • T. Machenry, G. Tudose, Reflections on symmetric polynomials and arithmetic functions, Rocky Mountain Journal of Mathematics 35 (3) (2006) 901–928.
  • T. Machenry, K. Wong, Degree k linear recursions mod(p) and number fields, Rocky Mountain Journal of Mathematics 41 (4) (2011) 1303–1327.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebir ve Sayı Teorisi
Bölüm Araştırma Makaleleri
Yazarlar

Yashwant Panwar

Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 24 Kasım 2023
Kabul Tarihi 25 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 4 Sayı: 2

Kaynak Göster

APA Panwar, Y. (2023). Some identities of bivariate Pell and bivariate Pell-Lucas polynomials. Journal of Amasya University the Institute of Sciences and Technology, 4(2), 90-99. https://doi.org/10.54559/jauist.1395447
AMA Panwar Y. Some identities of bivariate Pell and bivariate Pell-Lucas polynomials. J. Amasya Univ. Inst. Sci. Technol. Aralık 2023;4(2):90-99. doi:10.54559/jauist.1395447
Chicago Panwar, Yashwant. “Some Identities of Bivariate Pell and Bivariate Pell-Lucas Polynomials”. Journal of Amasya University the Institute of Sciences and Technology 4, sy. 2 (Aralık 2023): 90-99. https://doi.org/10.54559/jauist.1395447.
EndNote Panwar Y (01 Aralık 2023) Some identities of bivariate Pell and bivariate Pell-Lucas polynomials. Journal of Amasya University the Institute of Sciences and Technology 4 2 90–99.
IEEE Y. Panwar, “Some identities of bivariate Pell and bivariate Pell-Lucas polynomials”, J. Amasya Univ. Inst. Sci. Technol., c. 4, sy. 2, ss. 90–99, 2023, doi: 10.54559/jauist.1395447.
ISNAD Panwar, Yashwant. “Some Identities of Bivariate Pell and Bivariate Pell-Lucas Polynomials”. Journal of Amasya University the Institute of Sciences and Technology 4/2 (Aralık 2023), 90-99. https://doi.org/10.54559/jauist.1395447.
JAMA Panwar Y. Some identities of bivariate Pell and bivariate Pell-Lucas polynomials. J. Amasya Univ. Inst. Sci. Technol. 2023;4:90–99.
MLA Panwar, Yashwant. “Some Identities of Bivariate Pell and Bivariate Pell-Lucas Polynomials”. Journal of Amasya University the Institute of Sciences and Technology, c. 4, sy. 2, 2023, ss. 90-99, doi:10.54559/jauist.1395447.
Vancouver Panwar Y. Some identities of bivariate Pell and bivariate Pell-Lucas polynomials. J. Amasya Univ. Inst. Sci. Technol. 2023;4(2):90-9.
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