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Year 2023, Volume: 4 Issue: 2, 90 - 99, 31.12.2023

Yashwant Panwar

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

Abstract

References

  • 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

Year 2023, Volume: 4 Issue: 2, 90 - 99, 31.12.2023

Yashwant Panwar

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

Abstract

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.

Keywords

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

References

  • 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.
There are 11 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Research & Review Articles
Authors

Yashwant Panwar

Publication Date December 31, 2023
Submission Date November 24, 2023
Acceptance Date December 25, 2023
Published in Issue Year 2023 Volume: 4 Issue: 2

Cite

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. December 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, no. 2 (December 2023): 90-99. https://doi.org/10.54559/jauist.1395447.
EndNote Panwar Y (December 1, 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., vol. 4, no. 2, pp. 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 (December 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, vol. 4, no. 2, 2023, pp. 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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