GENERALIZED IDENTITIES OF BIVARIATE FIBONACCI AND BIVARIATE LUCAS POLYNOMIALS

Year 2020, Volume: 1 Issue: 2, 142 - 150, 31.12.2020

Yashwant Panwar , V. K. Gupta Jaya Bhandari

https://izlik.org/JA63UN74BM

Abstract

In this paper, we present generalized identities of bivariate Fibonacci polynomials and bivariate Lucas polynomials and related identities consisting even and odd terms. Binet’s formula will employ to obtain the identities. Also we describe and derive sums and connection formulae.

Keywords

Bivariate Fibonacci polynomials , Bivariate Lucas polynomials , Binet's formula

References

• Altıntaş, İ., & Taşköprü, K., (2019). Unoriented knot polynomials of torus links as Fibonacci-type polynomials. Asian-European Journal of Mathematics, 12(4). https://doi.org/10.1142/S1793557119500530
• Alves, F.R.V., & Catarino, P.M.M.C., (2016). The Bivariate (Complex) Fibonacci and Lucas Polynomials: An Historical Investigation with the Maple's Help. Acta Didactica Napocensia, 9(4), 71-95.
• Belbachir, H., & Bencherif, F. (2007). On some properties on bivariate Fibonacci and Lucas polynomials. arXiv:0710.1451v1
• Cakmak, T., & Karaduman, E., (2018). On the derivatives of bivariate Fibonacci polynomials. Notes On Number Theory and Discrete Mathematics, 24(3), 37-46.
• Catalani, M., (2004 ‘a’). Some Formulae for Bivariate Fibonacci and Lucas Polynomials. http://front.math.ucdavis.edu/math.CO/0406323
• Catalani, M., (2004 ‘b’). Identities for Fibonacci and Lucas Polynomials derived from a book of Gould. http://front.math.ucdavis.edu/math.CO/0407105
• Catalani, M., (2004 ‘c’). Generalized Bivariate Fibonacci Polynomials. Version 2, http://front.math.ucdavis.edu/math.CO/0211366
• Falcon, S., (2012). On k-Lucas numbers of arithmetic indexes. Applied Mathematics, 3, 1202-1206. http://dx.doi.org/10.4236/am.2012.310175
• Falcon, S., & Plaza, A., (2009). On k-Fibonacci numbers of arithmetic indexes. Applied Mathematics and Computation, 208, 180–185. doi:10.1016/j.amc.2008.11.031
• Inoue, K., & Aki, S., (2011). Bivariate Fibonacci polynomials of order k with statistical applications. Annals of the Institute of Statistical Mathematics, 63(1), 197-210.
• Jacob, G., Reutenauer, C., & Sakarovitch, J. (2006). On a divisibility property of Fibonacci polynomials. http://perso.telecom-paristech.fr/~jsaka/PUB/Files/DPFP.pdf
• Kaygisiz, K., & Sahin, A., (2011). Determinantal and permanental representation of generalized Bivariate Fibonacci p-polynomials. arXiv:1111.4071v1
• Panwar, Y. K., & Singh, M., (2014). Generalized bivariate Fibonacci-Like polynomials. International journal of Pure Mathematics, 1, 8-13.
• Tasci, D., Firengiz, M.C., & Tuglu, N. (2012). Incomplete Bivariate Fibonacci and Lucas 𝑝 –Polynomials. Discrete Dynamics in Nature and Society, vol. 2012, Article ID 840345, 2012. doi:10.1155/2012/840345.
• Taşköprü, K., & Altıntaş, İ., (2015). HOMFLY polynomials of torus links as generalized Fibonacci polynomials. The electronic journal of combinatorics, 22(4), #P4.8