On the Vieta–Jacobsthal-like polynomials

Wanna Sriprad, Somnuk Srisawat and Kitsana Charoenchaianan
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 9–19
DOI: 10.7546/nntdm.2022.28.1.9-19
Full paper (PDF, 195 Kb)

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Authors and affiliations

Wanna Sriprad
Department of Mathematics and Computer Science, Faculty of Science and Technology,
Rajamangala University of Technology, Thanyaburi, Pathum Thani 12110 Thailand

Somnuk Srisawat
Department of Mathematics and Computer Science, Faculty of Science and Technology,
Rajamangala University of Technology, Thanyaburi, Pathum Thani 12110 Thailand

Kitsana Charoenchaianan
Department of Mathematics and Computer Science, Faculty of Science and Technology,
Rajamangala University of Technology, Thanyaburi, Pathum Thani 12110 Thailand

Abstract

In this paper, we first introduce the generalization of the Vieta–Jacobsthal polynomial, which is called the Vieta–Jacobsthal-like polynomial. After that, we give the generating function, the Binet formula, and some well-known identities for this polynomial. Finally, we also present the relation between this polynomial and the previously famous Vieta polynomials.

Keywords

• Vieta–Jacobsthal polynomial
• Vieta–Jacobsthal–Lucas polynomial
• Generalized Vieta–Jacobsthal polynomial.

2020 Mathematics Subject Classification

• 11C08
• 11B39
• 33C45

References

1. Erkus-Duman, E., Tasci, D., & Yalcin, F. (2015). Generalized Vieta–Jacobsthal and Vieta–Jacobsthal–Lucas Polynomials. Mathematical Communications, 20, 241–251.
2. Horadam, A. F. (2002). Vieta polynomials. Fibonacci Quarterly, 40(3), 223–232.
3. Jacobsthal, E. (1955). Uber vertauschbare polynome. Mathematische Zeitschrift, 63, 244–276.
4. Kim, T., Kim, D. S., Dolgy, D. V., & Kwon, J. (2021). Sums of finite products of Chebyshev polynomials of two different types. AIMS Mathematics, 6(11), 12528–12542.
5. Kim, T., Kim, D. S., Dolgy, D. V., & Park, J.-W. (2018). Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials. Journal of Inequalities and Applications, Paper No. 148, 14 pp.
6. Robbins, N. (1991). Vieta’s triangular array and a related family of polynomials. International Journal of Mathematics and Mathematical Sciences, 14, 239–244.
7. Tasci, D., & Yalcin, V. (2013). Vieta–Pell and Vieta–Pell–Lucas polynomials. Advances in Difference Equations, 224, 1–8.

Manuscript history

• Received: 28 April 2021
• Revised: 20 January 2022
• Accepted: 27 January 2022
• Online First: 3 February 2022