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Homogeneous symmetric functions and new generating functions for products of some numbers with bivariate Mersenne and bivariate Mersenne Lucas polynomials | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 شهریور 1404 اصل مقاله (455.73 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.29817.2170 | ||
| نویسندگان | ||
| Amina Daoui1؛ Ali Boussayoud* 2؛ Noureddine Midoune3؛ khadidja Boubellouta2 | ||
| 1Department of Mathematics,University Ferhat Abbas Setif1, Algeria Laboratory of Mathematics and their Interactions, Abd el Hafidh Boussof University center of Mila, Algeria | ||
| 2LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria | ||
| 3Department of mathematics, M’sila University, M’sila, Algeria Laboratory of Pure and Applied Mathematics, Algeria | ||
| چکیده | ||
| The aim of this paper is to provide some operators for symmetric functions for the purpose of obtaining new generating functions for products of k-Fibonacci, $K$-Lucas and $k$-Jacobsthal numbers, $K$-Mersenne numbers bivariate complex Fibonacci poly nomials and Cheb yshev poly nomials with bivariate Mersenne and bivariate Mersenne Lucas polynomials . | ||
| کلیدواژهها | ||
| Generating functions؛ Bivariate Mersenne Lucas polynomials؛ k-Fibonacci numbers؛ k-Pell numbers؛ k-balancing numbers | ||
| مراجع | ||
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[1] A. Abderrezzak, Généralization de la transformation d’Euler d’une série formelle, Adv. Math. 103 (1994), no. 2, 180–195. https://doi.org/10.1006/aima.1994.1008
[2] B. Aloui and A. Boussayoud, Generating function of the product of the $k$-Fibonacci and $k$-Pell numbers and Chebyshev polynomials of the third and fourth kind, Eng. Sci. Aerosp. MESA 12 (2021), no. 1, 245–257.
[3] M. Asci and E. Gurel, On bivariate complex Fibonacci and Lucas polynomials, 2012, pp. 11–14.
[4] M. Asci and E. Gurel, Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers, Notes Number Theory Discrete Math. 19 (2013), no. 1, 25–36.
[5] K. Boubellouta, A. Boussayoud, and M. Kerada, Symmretric functions for second-order recurrence sequences, Tbilisi Math. J. 13 (2020), no. 2, 225–237. https://doi.org/10.32513/tbilisi/1593223230
[6] A. Boussayoud, A. Abderrezzak, and M. Kerada, Some applications of symmetric functions., Integers 15 (2015), no. 1, 1–7.
[7] A. Boussayoud and S. Boughaba, On some identities and generating functions for k-Pell sequences and Chebyshev polynomials, Online J. Anal. Comb 14 (2019), no. 3, 1–13.
[8] A. Boussayoud, S. Boughaba, M. Kerada, S. Araci, and M. Acikgoz, Generating functions of binary products of $k$-Fibonacci and orthogonal polynomials, Rev. Real Acad. Cienc. Exactas Fis. Nat. - A: Mat. 113 (2019), no. 3, 2575–2586. https://doi.org/10.1007/s13398-019-00641-4
[9] A. Boussayoud, M. Kerada, and R. Sahali, Symmetrizing operations on some orthogonal polynomials, Int. J. Pure Appl. Math 9 (2015), no. 3, 191–199.
[10] P. Catarino, On some identities and generating functions for k-Pell numbers, Int. J. Math. Anal.(Ruse) 7 (2013), no. 38, 1877–1884. http://doi.org/10.12988/ijma.2013.35131
[11] P. Catarino, On generating matrices of the $k$-Pell, $k$-Pell-Lucas and modified $k$-Pell sequences, Pure Math. Sci. 3 (2014), no. 2, 71–77. http://dx.doi.org/10.12988/pms.2014.411
[12] M. Chelgham and A. Boussayoud, On the $k$-Mersenne–Lucas numbers, Notes Number Theory Discrete Math. 27 (2021), no. 1, 7–13. https://doi.org/10.7546/nntdm.2021.27.1.7–13
[13] B.G.S. Doman and J.K. Williams, Fibonacci and Lucas polynomials, Math. Proc.Cambridge Philos. Soc. 90 (1981), no. 3, 385–387.
[14] M.R. Eslahchi, M. Dehghan, and S. Amani, The third and fourth kinds of Chebyshev polynomials and best uniform approximation, Math. Comput. Model. 55 (2012), no. 5-6, 1746–1762. https://doi.org/10.1016/j.mcm.2011.11.023
[15] S. Falcon and Á. Plaza, The $k$-Fibonacci sequence and the Pascal 2-triangle, Chaos Solit. Fractals 33 (2007), no. 1, 38–49. https://doi.org/10.1016/j.chaos.2006.10.022
[16] A.F. Horadam, Generating functions for powers of a certain generalised sequence of numbers, Duke Math. J. 32 (1965), no. 3, 437–446. http://dx.doi.org/10.1215/S0012-7094-65–03244-8
[17] A.F. Horadam and P. Filipponi, Derivative sequences of Jacobsthal and Jacobsthal-Lucas polynomials, Fibonacci Q. 35 (1997), no. 4, 352–357. https://doi.org/10.1080/00150517.1997.12428981
[18] A.F. Horadam and B.J.M. Mahon, Pell and Pell-Lucas polynomials, Fibonacci Q. 23 (1985), no. 1, 7–20. https://doi.org/10.1080/00150517.1985.12429849
[19] D. Jhala and G.P.S. Rathore, Some properties of the $k$-Jacobsthal Lucas sequence, Int. J. Modern Sci. Engin. Tech. 1 (2014), no. 3, 87–92.
[20] D. Jhala, K. Sisodiya, and G.P.S. Rathore, On some identities for $k$-Jacobsthal numbers, Int. J. Math. Anal.(Ruse) 7 (2013), no. 12, 551–556.
[21] H. Merzouk, A. Boussayoud, and M. Chelgham, Symmetric functions of generalized polynomials of second order, Turkish J. Analysis Number Theory 7 (2019), no. 5. 135-139.
[22] N. Saba and A. Boussayoud, On the bivariate Mersenne Lucas polynomials and their properties, Chaos Solit. Fractals 146 (2021), 110899. https://doi.org/10.1016/j.chaos.2021.110899
[23] N. Saba, A. Boussayoud, and K.V.V. Kanuri, Mersenne Lucas numbers and complete homogeneous symmetric functions, J. Math. Comput. Sci 24 (2021), no. 2, 127–139. http://doi.org/10.22436/jmcs.024.02.04
[24] K. Uslu and V. Deniz, Some identities of k-Mersenne numbers, Adv. Appl. Discrete Math. 18 (2017), no. 4, 413. https://doi.org/10.17654/DM018040413 | ||
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