Browse > Article
http://dx.doi.org/10.14317/jami.2022.243

NEW THEOREM ON SYMMETRIC FUNCTIONS AND THEIR APPLICATIONS ON SOME (p, q)-NUMBERS  

SABA, N. (LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University)
BOUSSAYOUD, A. (LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University)
Publication Information
Journal of applied mathematics & informatics / v.40, no.1_2, 2022 , pp. 243-257 More about this Journal
Abstract
In this paper, we present and prove an new theorem on symmetric functions. By using this theorem, we derive some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q)-Jacobsthal Lucas numbers with Chebyshev polynomials of the first kind.
Keywords
Symmetric functions; generating functions; (p, q)-Lucas numbers; (p, q)-Jacobsthal numbers; k-Fibonacci numbers; Chebyshev polynomials of the first kind; Pell polynomials;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 G.B. Djordjevic, H.M. Srivastava, Some generalizations of certain sequences associated with the Fibonacci numbers, J. Indonesian Math. Soc. 12 (2006), 99-112.
2 A. Boussayoud, M. Kerada, R. Sahali, Symmetrizing operations on some orthogonal polynomials, Int. Electron. J. Pure Appl. Math. 9 (2015), 191-199.
3 A.F. Horadam, J.M. Mahon, Pell and Pell-Lucas polynomials, Fibonacci Q. 23 (1985), 7-20.
4 A. Suvarnamani, M. Tatong, Some properties of (p, q)-Fibonacci numbers, Science and Technology RMUTT Journal 5 (2015), 17-21.
5 A. Abderrezzak, Generalisation de la transformation d'Euler d'une serie formelle, Adv. Math. 103 (1994), 180-195.   DOI
6 A. Boussayoud, M. Kerada, Symmetric and generating functions, Int. Electron. J. Pure Appl. Math. 7 (2014), 195-203.
7 A. Benoit, Algorithmique semi-numerique rapide des series de Tchebychev, HAL Id: pastel-00726487, https://pastel.archives-ouvertes.fr/pastel-00726487, 2012.
8 A. Boussayoud, M. Kerada, N. Harrouche, On the k-Lucas numbers and Lucas polynomials, Turkish Journal of Analysis and Number 5 (2017), 121-125.   DOI
9 H.H. Gulec, N. Taskara, On the (s, t)-Pell and (s, t)-Pell Lucas sequences and their matrix representations, Appl. Math. Lett. 25 (2012), 1554-1559.   DOI
10 H.M. Srivastava, N. Tuglu, M. Cetin, Some results on the q-analogues of the incomplete Fibonacci and Lucas polynomials, Miskolc Math. Notes 20 (2019), 511-524.   DOI
11 A. Boussayoud, M. Kerada, R. Sahali, W. Rouibah, Some applications on generating functions, J. Concr. Appl. Math. 12 (2014), 321-330.
12 A.F. Horadam, A generalized Fibonacci sequence, Am. Math. Mon. 68 (1961), 455-459.   DOI
13 A. Suvarnamani, Some properties of (p, q)-Lucas numbers, Kyungpook Math. J. 56 (2016), 367-370.   DOI
14 G.B. Djordjevic, H.M. Srivastava, Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers, Math. Comput. Model. 42 (2005), 1049-1056.   DOI
15 N. Saba, A. Boussayoud, Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials, Open J. Math. Sci. 4 (2020), 179-185.   DOI
16 N. Saba, A. Boussayoud, A. Abderrezzak, Complete homogeneous symmetric functions of third and second-order linear recurrence sequences, Electron. J. Math. Analysis Appl. 9 (2021), 221-245.
17 N. Saba, A. Boussayoud, M. Chelgham, Symmetric and generating functions for some generalized polynomials, Malaya Journal of Mathematik 8 (2020), 1756-1765.   DOI
18 I. Gosai, Fibonacci sequence and it's applications, International Journal of Research and Analytical Reviews (IJRAR) 6 (2019), 241-247.
19 M. Shafiq, H.M. Srivastava, N. Khan, Q.Z. Ahmad, M. Darus, S. Kiran, An upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with k-Fibonacci numbers, Symmetry 12 (2020), 1-17.   DOI
20 N. Saba, A. Boussayoud, K.V.V. Kanuri, Mersenne Lucas numbers and complete homogeneous symmetric functions, J. Math. Computer Sci. 24 (2022), 127-139.
21 N. Saba, A. Boussayoud, M. Kerada, Generating functions of even and odd Gaussian numbers and polynomials, J. Sci. Arts. 1 (2021), 125-144.
22 N. Saba, A. Boussayoud, Symmetric and generating functions of generalized (p, q)-numbers, Kuwait J. Sci. 48 (2021), 1-15.
23 N. Saba, A. Boussayoud, M. Ferkioui, S. Boughaba, Symmetric functions of binary products of Gaussian Jacobsthal Lucas polynomials and Chebyshev polynomials, Palest. J. Math. 10 (2021), 452-464.
24 N. Saba, A. Boussayoud, Ordinary generating functions of binary products of (p, q)-modified Pell numbers and k-numbers at positive and negative indices, J. Sci. Arts. 3 (2020), 627-648.
25 S. Falcon, A. Plaza, The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solitons & Fractals 33 (2008), 38-49.   DOI
26 S. Uygun, The (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas sequences, Appl. Math. Sci. 9 (2015), 3467-3476.