Jacobsthal representation hybrinomials



Abstract

Jacobsthal numbers are a special case of numbers defined recursively by the second order linear relation and for these reasons they are also named as numbers of the Fibonacci type. They have many interpretations, representations and applications in distinct areas of mathematics. In this paper we present the Jacobsthal representation hybrinomials, i.e. polynomials, which are a generalization of Jacobsthal hybrid numbers.


Keywords

Jacobsthal numbers; recurrence relations; complex numbers; hyperbolic numbers; dual numbers; polynomials

1. G. Anatriello and G. Vincenzi, On h-Jacobsthal and h-Jacobsthal–Lucas sequences, and related quaternions, An. Ştiinţ. Univ. “Ovidius” Constanţa 27 (2019), no. 3, 5–23.
2. G.B. Djordjevic, Generalized Jacobsthal polynomials, Fibonacci Quart. 38 (2000), no. 3, 239–243.
3. A.F. Horadam, Jacobsthal and Pell curves, Fibonacci Quart. 26 (1988), no. 1, 77–83.
4. A.F. Horadam, Jacobsthal representation numbers, Fibonacci Quart. 34 (1996), no. 1, 40–54.
5. A.F. Horadam, Jacobsthal representation polynomials, Fibonacci Quart. 35 (1997), no. 2, 137–148.
6. T. Horzum and E.G. Kocer, On some properties of Horadam polynomials, Int. Math. Forum 4 (2009), no. 25, 1243–1252.
7. M. Liana, A. Szynal-Liana, and I. Włoch, On Pell hybrinomials, Miskolc Math. Notes 20 (2019), no. 2, 1051–1062.
8. M. Özdemir, Introduction to hybrid numbers, Adv. Appl. Clifford Algebr. 28 (2018), no. 1, Paper No. 11, 32 pp.
9. A. Szynal-Liana, The Horadam hybrid numbers, Discuss. Math. Gen. Algebra Appl. 38 (2018), no. 1, 91–98.
10. A. Szynal-Liana, A. Włoch, and I. Włoch, On generalized Pell numbers generated by Fibonacci and Lucas numbers, Ars Combin. 115 (2014), 411–423.
11. A. Szynal-Liana and I. Włoch, Hypercomplex Numbers of the Fibonacci Type, Oficyna Wydawnicza Politechniki Rzeszowskiej, Rzeszów, 2019.
12. A. Szynal-Liana and I. Włoch, On Jacobsthal and Jacobsthal–Lucas hybrid numbers, Ann. Math. Sil. 33 (2019), 276–283.
13. A. Szynal-Liana and I. Włoch, Introduction to Fibonacci and Lucas hybrinomials, Complex Var. Elliptic Equ. 65 (2020), no. 10, 1736–1747.
Download

Published : 2021-11-27


LianaM., Szynal-LianaA., & WłochI. (2021). Jacobsthal representation hybrinomials. Annales Mathematicae Silesianae, 36(1), 57-70. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/13461

Mirosław Liana 
Politechnika Rzeszowska, Wydział Zarządzania  Poland
Anetta Szynal-Liana  aszynal@prz.edu.pl
Politechnika Rzeszowska, Wydział Matematyki i Fizyki Stosowanej  Poland
https://orcid.org/0000-0001-5508-0640
Iwona Włoch 
Politechnika Rzeszowska, Wydział Matematyki i Fizyki Stosowanej  Poland



The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

  1. License
    This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
  2. Author’s Warranties
    The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
  3. User Rights
    Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
  4. Co-Authorship
    If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.