Generating Functions of Binary Products of Tribonacci and Tribonacci Lucas Polynomials and Special Numbers

  • Hind Merzouk LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria
  • Ali Boussayoud LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria
  • Kasi Viswanadh V. Kanuri 3669 Leatherwood Dr, Frisco, TX 75033, USA
Keywords: Tribonacci polynomials, k-Fibonacci numbers,, k-Pell numbers, generating function

Abstract

In this paper, we introduce a new operator defined in this paper, we give some new generating functions of binary products of Tribonacci and Tribonacci Lucas polynomials and special numbers.

References

A. Boussayoud and S. Boughaba, On some identities and generating functions for k-Pell sequences and Chebyshev polynomials, Online J. Anal. Comb. 14(3) (2019), 1-13.

A. Boussayoud and A. Abderrezzak, Complete homogeneous symmetric functions and Hadamard product, Ars Comb. 144 (2019), 81-90.

A. Boussayoud, M. Chelgham, S. Boughaba, On some identities and generating functions for Mersenne numbers and polynomials, Turkish Journal of Analysis and Number Theory 6(3) (2018), 93-97. https://doi.org/10.12691/tjant-6-3-5

A. Boussayoud, M. Bolyer and M. Kerada, On some identities and symmetric functions for Lucas and Pell numbers, Electron. J. Math. Analysis Appl. 5 (2017), 202-207.

A. Boussayoud, M. Kerada and N. Harrouche, On the k-Lucas numbers and Lucas polynomials, Turkish Journal of Analysis and Number 5 (2017), 121-125. https://doi.org/10.12691/tjant-5-4-1

A. Boussayoud, On some identities and generating functions for Pell-Lucas numbers, Online. J. Anal. Comb. 12(1) (2017), 1-10.

A. Boussayoud, M. Kerada and M. Boulyer, A simple and accurate method for determination of some generalized sequence of numbers, Int. J. Pure Appl. Math. 108 (2016), 503-511.

A. Boussayoud, M. Kerada and R. Sahali, Symmetrizing operations on some orthogonal polynomials, Int. Electron. J. Pure Appl. Math. 9 (2015), 191-199. http://dx.doi.org/10.12732/iejpam.v9i3.8

A. Boussayoud and R. Sahali, The application of the operator ${small L}_{b_{1}b_{2}}^{-k}$ {small in the series }$dsumlimits_{j=0}^{infty }{small a}_{j}{small b}_{1}^{j}{small z}^{j}$, J. Adv. Res. Appl. Math. 7 (2015), 68-75.

A. Boussayoud and M. Kerada, Symmetric and generating functions, Int. Electron. J. Pure Appl. Math. 7 (2014), 195-203.

A. Pintér and H.M. Srivastava, Generating functions of the incomplete Fibonacci and Lucas numbers, Rend. Circ. Mat. Palermo 48 (1999), 591-596.https://doi.org/10.1007/BF02844348

D. Tasci and M. Cetin Firengiz, Incomplete Fibonacci and Lucas p-numbers, Math. Comput. Model. 52 (2010), 1763-1770. https://doi.org/10.1016/j.mcm.2010.07.003

G.B. Djordjevic, Generating functions of the incomplete generalized Fibonacci and generalized Lucas numbers, Fibonacci Q. 42 (2004), 106-113.

G.B. Djordjevic and H.M. Srivastava, Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers, Math. Comput. Model. 42 (2005), 1049-1056. https://doi.org/10.1016/j.mcm.2004.10.026.

P. Catarino, On some identities and generating functions for k-Pell numbers, Int. J. Math. Anal. 7 (2013), 1877-1884. http://dx.doi.org/10.12988/ijma.2013.35131

S. Boughaba, A. Boussayoud and M. Kerada, Construction of symmetric functions of generalized Fibonacci numbers, Tamap Journal of Mathematics and Statistics 3 (2019), 1-7. https://doi.org/10.29371/2019.16.SI01

S. Falcon and A. Plaza, On the Fibonacci k-numbers, Chaos Solit. Fract. 32 (2007), 1615-1624. https://doi.org/10.1016/j.chaos.2006.09.022

H. Merzouk, A. Boussayoud and M. Chelgham, Symmetric functions of binary products of Tribonacci Lucas numbers and orthogonal polynomials, J. Sci. Arts 2(55) (2021), 461-478. https://doi.org/10.46939/J.Sci.Arts-21.2-a13

H. Merzouk, B. Aloui and A. Boussayoud, Generating functions of the products of 2-orthogonal Chebyshev polynomials with some numbers and the other Chebyshev polynomials, Issues of Analysis 10(28)(1) (2021),17-33. https://doi.org/ 10.15393/j3.art.2021.8530

H. Merzouk, A. Boussayoud and M. Chelgham, Generating functions of generalized Tribonacci and Tricobsthal polynomials, Montes Taurus J. Pure Appl. Math. 2(2) (2020), 7-37.

H. Merzouk, A. Boussayoud and M. Chelgham, Symmetric functions of generalized polynomials of second order, Turkish Journal of Analysis and Number 7(5) (2019), 135. https://doi.org/10.12691/tjant-7-5-2

Jr. V.E. Hoggatt and M. Bicknell, Generalized Fibonacci polynomials, Fibonacci Quarterly 11 (1973), 457-465.

N. Saba and A. Boussayoud, Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials, Open J. Math. Sci. 4 (2020), 179-185. https://doi.org/10.30538/oms2020.0108

N. Yilmaz and N. Taskara, Incomplete Tribonacci-Lucas numbers and polynomials, arXiv:1404.4168v1 [math.NT] (16 Apr 2014).

Y. Ben Cheikh and N. Ben Romhane, d-orthogonal polynomials sets of Tchebytchev type, in: Proceedings of the International Conference on Difference Equations, Special Functions and Orthogonal Polynomials, S. Elaydi et al. (Ed.), Munich, Germany, 25-30 July 2005, World Scientific. https://doi.org/10.1142/9789812770752_0008

Published
2022-01-16
How to Cite
Merzouk, H., Boussayoud, A., & Kanuri, K. V. V. (2022). Generating Functions of Binary Products of Tribonacci and Tribonacci Lucas Polynomials and Special Numbers. Earthline Journal of Mathematical Sciences, 8(2), 237-262. https://doi.org/10.34198/ejms.8222.237262
Section
Articles