Affiliation:
1. Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey
Abstract
In this paper, we investigate the generalized Tribonacci polynomials and we deal with, in detail, two special cases which we call them (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials. We also introduce and investigate a new sequence and its two special cases namely the generalized co-Tribonacci, (r,s,t)-co-Tribonacci and (r,s,t)-co-Tribonacci-Lucas polynomials, respectively. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices related to these polynomials. Furthermore, we evaluate the infinite sums of special cases of (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials.
Reference19 articles.
1. D. Andrica and O. Bagdasar, Recurrent Sequences : Key Results, Applications, and Problems, Springer, 2020. https://doi.org/10.1007/978-3-030-51502-7
2. G. Cerda-Moralez, On third-order Jacobsthal polynomials and their properties, Miskolc Mathematical Notes 22(1) (2021), 123-132. https://doi.org/10.18514/mmn.2021.3227
3. G.B. Djordjević and G.V. Milovanović, Special Classes of Polynomials, University of Niš, Faculty of Technology, Leskovac, 2014. http://www.mi.sanu.ac.rs/~gvm/Teze/Special_0Classes_of_Polynomials.pdf
4. G. Frei, Binary Lucas and Fibonacci Polynomials, I, Math. Nachr. 96 (1980), 83-112. https://doi.org/10.1002/mana.19800960109
5. R. Flórez, N. McAnally and A. Mukherjee, Identities for the Generalized Fibonacci Polynomial, Integers 18B (2018).
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