On Some Identities and Symmetric Functions for Balancing Numbers

Ali Boussayoud

Araştırma Makalesi

On Some Identities and Symmetric Functions for Balancing Numbers

Yıl 2018, Sayı: 23, 68 - 77, 01.06.2018

Öz

In this paper, we derive
new generating functions of the product of balancing numbers, Lucas balancing
numbers and the Chebychev polynomials of the second kind by making use of
useful properties of the symmetric functions mentioned in the paper.

Anahtar Kelimeler

Balancing numbers, Lucas balancing number, Chebychev polynomials

Kaynakça

[1] A. Behera, G. K. Panda, On the Square Roots of Triangular Numbers. The Fibonacci Quarterly. 37, 98-105, (1999).
[2] A. Boussayoud, M. Kerada, N. Harrouche, On the k-Lucas numbers and Lucas Polynomials, Turkish Journal of Analysis and Number. 5(3) 121-125, (2017).
[3] A. Boussayoud, M. Bolyer, M. Kerada, On Some Identities and Symmetric Functions for lucas and pell numbers, Electron. J. Math. Analysis Appl. 5(1), 202-207, (2017).
[4] A. Boussayoud, On some identities and generating functions for Pell-Lucas numbers, Online.J. Anal. Comb. 12 1-10, (2017).
[5] A. Boussayoud, N. Harrouche, Complete Symmetric Functions and k-Fibonacci Numbers, Commun. Appl. Anal. 20, 457-467, (2016).
[6] A. Boussayoud, M. Boulyer, M. Kerada, A simple and accurate method for determination of some generalized sequence of numbers, Int. J. Pure Appl. Math. 108, 503-511, (2016).
[7] A. Boussayoud, A. Abderrezzak, M. Kerada, Some applications of symmetric functions, Integers. 15, A#48, 1-7, (2015).
[8] A. Boussayoud, M. Kerada, R. Sahali , W. Rouibah, Some Applications on Generating Functions, J. Concr. Appl. Math. 12, 321-330, (2014).
[9] A. Boussayoud, M. Kerada, Symmetric and Generating Functions, Int. Electron. J. Pure Appl. Math. 7, 195-203 (2014).
[10] P. Catarino, H. Campos, P. Vasco, On the Mersenne sequence, Ann. Math. Inform. 46, 37- 53, (2016).
[11] V. E. Hoggatt, Fibonacci and Lucas Numbers. A publication of the Fibonacci Association. University of Santa Clara, Santa Clara, Houghton Mifflin Company, 1969.
[12] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley, New York, 2001.
[13] T. Koshy, Z. Gao, Catalan numbers with Mersenne subscripts, Math. Sci. 38, 86-91, (2013).
[14] A. Ozkoc, A. Tekcan, On k-balancing numbers, Noteson Number Theory and Discrete Mathematics. 20, 38-52, (2017).

Yıl 2018, Sayı: 23, 68 - 77, 01.06.2018

Ali Boussayoud

Öz

Kaynakça

[1] A. Behera, G. K. Panda, On the Square Roots of Triangular Numbers. The Fibonacci Quarterly. 37, 98-105, (1999).
[2] A. Boussayoud, M. Kerada, N. Harrouche, On the k-Lucas numbers and Lucas Polynomials, Turkish Journal of Analysis and Number. 5(3) 121-125, (2017).
[3] A. Boussayoud, M. Bolyer, M. Kerada, On Some Identities and Symmetric Functions for lucas and pell numbers, Electron. J. Math. Analysis Appl. 5(1), 202-207, (2017).
[4] A. Boussayoud, On some identities and generating functions for Pell-Lucas numbers, Online.J. Anal. Comb. 12 1-10, (2017).
[5] A. Boussayoud, N. Harrouche, Complete Symmetric Functions and k-Fibonacci Numbers, Commun. Appl. Anal. 20, 457-467, (2016).
[6] A. Boussayoud, M. Boulyer, M. Kerada, A simple and accurate method for determination of some generalized sequence of numbers, Int. J. Pure Appl. Math. 108, 503-511, (2016).
[7] A. Boussayoud, A. Abderrezzak, M. Kerada, Some applications of symmetric functions, Integers. 15, A#48, 1-7, (2015).
[8] A. Boussayoud, M. Kerada, R. Sahali , W. Rouibah, Some Applications on Generating Functions, J. Concr. Appl. Math. 12, 321-330, (2014).
[9] A. Boussayoud, M. Kerada, Symmetric and Generating Functions, Int. Electron. J. Pure Appl. Math. 7, 195-203 (2014).
[10] P. Catarino, H. Campos, P. Vasco, On the Mersenne sequence, Ann. Math. Inform. 46, 37- 53, (2016).
[11] V. E. Hoggatt, Fibonacci and Lucas Numbers. A publication of the Fibonacci Association. University of Santa Clara, Santa Clara, Houghton Mifflin Company, 1969.
[12] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley, New York, 2001.
[13] T. Koshy, Z. Gao, Catalan numbers with Mersenne subscripts, Math. Sci. 38, 86-91, (2013).
[14] A. Ozkoc, A. Tekcan, On k-balancing numbers, Noteson Number Theory and Discrete Mathematics. 20, 38-52, (2017).

Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Araştırma Makalesi
Yazarlar	Ali Boussayoud
Yayımlanma Tarihi	1 Haziran 2018
Gönderilme Tarihi	26 Nisan 2018
Yayımlandığı Sayı	Yıl 2018 Sayı: 23

Kaynak Göster

APA	Boussayoud, A. (2018). On Some Identities and Symmetric Functions for Balancing Numbers. Journal of New Theory(23), 68-77.
AMA	Boussayoud A. On Some Identities and Symmetric Functions for Balancing Numbers. JNT. Haziran 2018;(23):68-77.
Chicago	Boussayoud, Ali. “On Some Identities and Symmetric Functions for Balancing Numbers”. Journal of New Theory, sy. 23 (Haziran 2018): 68-77.
EndNote	Boussayoud A (01 Haziran 2018) On Some Identities and Symmetric Functions for Balancing Numbers. Journal of New Theory 23 68–77.
IEEE	A. Boussayoud, “On Some Identities and Symmetric Functions for Balancing Numbers”, JNT, sy. 23, ss. 68–77, Haziran 2018.
ISNAD	Boussayoud, Ali. “On Some Identities and Symmetric Functions for Balancing Numbers”. Journal of New Theory 23 (Haziran 2018), 68-77.
JAMA	Boussayoud A. On Some Identities and Symmetric Functions for Balancing Numbers. JNT. 2018;:68–77.
MLA	Boussayoud, Ali. “On Some Identities and Symmetric Functions for Balancing Numbers”. Journal of New Theory, sy. 23, 2018, ss. 68-77.
Vancouver	Boussayoud A. On Some Identities and Symmetric Functions for Balancing Numbers. JNT. 2018(23):68-77.