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Construction of generating functions of the products of Vieta polynomials with Gaussian numbers and polynomials | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 50، دوره 12، شماره 1، مرداد 2021، صفحه 649-668 اصل مقاله (426.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4868 | ||
| نویسندگان | ||
| Souhila Boughaba1؛ Nabiha Saba2؛ Ali Boussayoud* 3 | ||
| 1LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria | ||
| 2LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria | ||
| 3LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria. | ||
| تاریخ دریافت: 18 فروردین 1399، تاریخ بازنگری: 07 مهر 1399، تاریخ پذیرش: 25 آذر 1399 | ||
| چکیده | ||
| In the present paper, we introduce the recurrence relations of Vieta Fibonacci, Vieta Lucas, Vieta Pell and Vieta Pell Lucas polynomials. We obtain the generating functions of these polynomials, then we give the new generating functions of the products of these polynomials and the products of these polynomials with Gaussian numbers and polynomials. These results are based on the relation between Vieta polynomials and Chebyshev polynomials of first and second kinds. | ||
| کلیدواژهها | ||
| Generating functions؛ Vieta Fibonacci polynomials؛ Vieta Lucas polynomials؛ Vieta Pell polynomials؛ Gaussian numbers | ||
| مراجع | ||
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[1] A. Boussayoud, On some identities and generating functions for Pell Lucas numbers, Online J. Anal. Comb. 12 (2017) 1–10. [2] A. Boussayoud, M. Boulyer and M. Kerada, A simple and accurate method for determination of some generalized sequence of numbers, Int. J. Pure Appl. Math.108 (2016) 503–511. [3] A. Boussayoud, Laction de l’operateur δke1e2 sur la serie ∑n=0∞=Sn(A)en1zn, Doctoral dissertation, Mohamed Seddik Ben Yahia University, Jijel, Algeria, 2017. [4] A. Boussayoud, A. Abderrezzak and M. Kerada, Some applications of symmetric functions, Integers. 15 (2015)1–7. [5] A. F. Horadam, Vieta Polynomials, Fibonacci Q. 40 (2002) 223–232. [6] D. Tasci and F. Yalcin, Vieta-Pell and Vieta-Pell-Lucas polynomials, Adv. in Difference Equ, 2013. [7] E. Jacobsthal, Uber vertauschbare polynome. Math. Z. 63 (1955) 244–276. [8] N. Robbins, Vieta’s triangular array and a related family of polynomials, Int. J. Math. Math. Sci. 14 (1991) 239–244. [9] N. Saba, M. Ferkioui, A. Boussayoud and S. Boughaba, Symmetric Functions of Binary Products of Gaussian Jacobsthal Lucas Polynomials and Chebyshev Polynomials, Palest. J. Math (accepted). [10] S. Boughaba and A. Boussayoud, On Some Identities and Generating Function of Both K-jacobsthal Numbers and Symmetric Functions in Several Variables, Konuralp J. Math. 7 (2019) 235–242. [11] S. Boughaba and A. Boussayoud, Construction of Symmetric Functions of Generalized Fibonacci Numbers, Tamap Journal of Mathematics and Statistics. 3 (2019) 1–8. [12] S. Boughaba, A. Boussayoud and Kh. Boubellouta, Generating Functions of Modified Pell Numbers and Bivariate Complex Fibonacci Polynomials, Turkish Journal of Analysis and Number. 7 (2019) 113–116. [13] S. Boughaba, H. Merzouk, A. Boussayoud and N. Saba, Generating functions of the products of Gaussian Numbers with Chebyshev Polynomials of First and Second Kind, Transactions Issue Mathematics (Submitted). [14] J. H. Jordan, Gaussian Fibonacci and Lucas numbers, Fibonacci Q. 3 (1965) 315–318. [15] M. Asci and E. Gurel, Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials, Notes Number Theory Discrete Math. 19 (2013) 25–36. [16] I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, Oxford (1979). [17] S. Halici and S. Oz, On Some Gaussian Pell and Pell-Lucas Numbers, Ordu Univ. J. Sci. Tech. 6 (2016) 8–18. [18] S. Halici and S. Oz, On Gaussian Pell Polynomials and Their Some Properties, Palest. J. Math. 7 (2018) 251–256. [19] R. Vitula and D. Slota, On modified Chebyshev polynomials. J. Math. Anal. Appl. 324 (2006) 321–343. | ||
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