Research Article
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On Some Identities and Symmetric Functions for Balancing Numbers

Year 2018, Issue: 23, 68 - 77, 01.06.2018

Abstract

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.

References

  • [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).

Year 2018, Issue: 23, 68 - 77, 01.06.2018

Abstract

References

  • [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).
There are 14 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ali Boussayoud

Submission Date April 26, 2018
Publication Date June 1, 2018
Published in Issue Year 2018 Issue: 23

Cite

APA Boussayoud, A. (2018). On Some Identities and Symmetric Functions for Balancing Numbers. Journal of New Theory, 23, 68-77. https://izlik.org/JA37AB84ZH
AMA 1.Boussayoud A. On Some Identities and Symmetric Functions for Balancing Numbers. JNT. 2018;(23):68-77. https://izlik.org/JA37AB84ZH
Chicago Boussayoud, Ali. 2018. “On Some Identities and Symmetric Functions for Balancing Numbers”. Journal of New Theory, nos. 23: 68-77. https://izlik.org/JA37AB84ZH.
EndNote Boussayoud A (June 1, 2018) On Some Identities and Symmetric Functions for Balancing Numbers. Journal of New Theory 23 68–77.
IEEE [1]A. Boussayoud, “On Some Identities and Symmetric Functions for Balancing Numbers”, JNT, no. 23, pp. 68–77, June 2018, [Online]. Available: https://izlik.org/JA37AB84ZH
ISNAD Boussayoud, Ali. “On Some Identities and Symmetric Functions for Balancing Numbers”. Journal of New Theory. 23 (June 1, 2018): 68-77. https://izlik.org/JA37AB84ZH.
JAMA 1.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, no. 23, June 2018, pp. 68-77, https://izlik.org/JA37AB84ZH.
Vancouver 1.Boussayoud A. On Some Identities and Symmetric Functions for Balancing Numbers. JNT [Internet]. 2018 June 1;(23):68-77. Available from: https://izlik.org/JA37AB84ZH


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