A new symmetric endomorphism operator for some generalizations of certain generating functions

Ali Boussayoud, Abdelhamid Abderrezzak and Serkan Araci
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 4, Pages 45—58
DOI: 10.7546/nntdm.2018.24.4.45-58
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Authors and affiliations

Ali Boussayoud
LMAM-Department of Mathematics
Mohamed Seddik Ben Yahia University, Jijel, Algeria

Abdelhamid Abderrezzak
University of Paris 7, LITP
Place Jussieu, Paris cedex 05, France

Serkan Araci
Department of Economics, Faculty of Economics, Administrative and Social Sciences
Hasan Kalyoncu University, TR-27410, Gaziantep, Turkey


In this article, we introduce new symmetric endomorphism operators by making use of appropriate infinite product series. The main results show that after direct calculations, the proposed operators are qualified to obtain generating functions for k-Jacobsthal numbers and Tchebychev polynomials of the first and second kind.


  • Symmetric functions
  • Mersenne numbers
  • k-Jacobsthal numbers

2010 Mathematics Subject Classification

  • 05A15
  • 05E05
  • 11B39


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Cite this paper

Boussayoud, A., Abderrezzak, A., & Araci, S. (2018). A new symmetric endomorphism operator for some generalizations of certain generating functions. Notes on Number Theory and Discrete Mathematics, 24(4), 45-58, doi: 10.7546/nntdm.2018.24.4.45-58.

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