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
References
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.
Politechnika Rzeszowska, Wydział Zarządzania Poland
Politechnika Rzeszowska, Wydział Matematyki i Fizyki Stosowanej Poland
https://orcid.org/0000-0001-5508-0640
Politechnika Rzeszowska, Wydział Matematyki i Fizyki Stosowanej Poland
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