Symmetric and generating functions of generalized (p,q)-numbers
DOI:
https://doi.org/10.48129/kjs.v48i4.10074Keywords:
Symmetric functions, Generating functions, Generalized (p, q)-numbers, (p, q)-Pell numbers, q)-Jacobsthal numbers, Bivariate complex Fibonacci polynomialsAbstract
In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions 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. After that, we give some new generating functions for product of (p,q)-numbers with bivariate complex Fibonacci and Lucas polynomials.References
A. Abderrezzak, Généralisation de la transformation dEuler dune série formelle. Adv. Math. 103, 180195, 1994.
A. Boussayoud, S. Boughaba, M. Kerada, S. Araci, M. Acikgoz, Generating functions of binary products of
k-Fibonacci and orthogonal polynomials, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM. 113,
2586, 2019.
A. Boussayoud, S. Boughaba, On some identities and generating functions for k-Pell sequences and Chebyshev
polynomials, Online J. Anal. Comb. 14, 113, 2019.
A. Boussayoud, A. Abderrezzak, Complete homogeneous symmetric functions and Hadamard product, Ars Comb.
, 8190, 2019.
A. Boussayoud, Laction de lopérateur ke
e2 sur la série 1P
n =0
Sn(A)en1
zn. (Doctoral dissertation), Mohamed Seddik
Ben Yahia University, Jijel, Algeria (2017).
A. Boussayoud, On some identities and generating functions for Pell-Lucas numbers, Online J. Anal. Comb. 12,
10, 2017.
A. Boussayoud, M. Kerada, Symmetric and generating functions, Int. Electron. J. Pure Appl. Math. 7, 195203,
A. Boussayoud, M. Kerada, R. Sahali, W. Rouibah, Some applications on generating functions, J. Concr. Appl.
Math. 12, 321330, 2014.
A. Suvarnamani, Some identities of (p; q)-Fibonacci numbers by Matrix methods. Phranakhon Rajabhat Research
Journal (Science and Technology), 12, 4953, 2017.
A. Suvarnamani, M. Tatong, Some properties of the product of (p; q)-Fibonacci and (p; q)-Lucas numbers, Inter-
national Journal of GEOMATE. 13, 1619, 2017.
A. Suvarnamani, On the odd and even terms of (p; q)-Fibonacci numbers and (p; q)-Lucas numbers, NSRU Science
and Technology Journal, 8, 7378, 2016.
A. Suvarnamani, Some properties of (p; q)-Lucas numbers, Kyungpook Math. J. 56, 367370, 2016.
A. Suvarnamani, M. Tatong, Some properties of (p; q)-Fibonacci numbers, Science and Technology RMUTT
Journal. 5, 1721, 2015.
H. H. Gulec, N. Taskara, On the (s; t)-Pell and (s; t)-Pell Lucas sequences and their matrix representations, Appl.
Math. Lett. 25, 15541559, 2012.
S. Boughaba, A. Boussayoud, Kh. Boubellouta, Generating functions of modi ed Pell numbers and bivariate
complex Fibonacci polynomials, Turkish Journal of Analysis and Number. 7, 113116, 2019.
M. Asci, E. Gurel, On bivariate complex Fibonacci and Lucas polynomials, Conference on Mathematical Sciences
ICM 2012, March 1114, 2012.
I. G. Macdonald, Symmetric functions and Hall polynomias. Oxford University Press, Oxford (1979).
S. Uygin, The (s; t)-Jacobsthal and (s; t)-Jacobsthal Lucas sequences, Appl. Math. Sci. 9, 34673476, 2015.
