Affiliation:
1. DÜZCE ÜNİVERSİTESİ
2. YILDIZ TEKNİK ÜNİVERSİTESİ
Abstract
In this present study, we intend to determine the Padovan, Perrin and Pell-Padovan dual quaternions with nonnegative and negative subscripts. In line with this purpose, we construct some new properties such as; special determinant equalities, new recurrence relations, matrix formulas, Binet-like formulas, generating functions, exponential generating functions, summation formulas, and binomial properties for these special dual quaternions.
Publisher
Turkish Journal of Mathematics and Computer Science, Association of Mathematicians
Reference49 articles.
1. Atanassov, K., Dimitrov, D., Shannon, A., A remark on $\psi$-function and Pell-Padovan's sequence, Notes on Number Theory and Discrete Mathematics, 15 (2009) 1-44.
2. Bilgici, G., Generalized order-$k$ Pell-Padovan-like numbers by matrix methods, Pure and Applied Mathematics Journal, 2(6) (2013), 174-178.
3. Cerda-Morales, G., Dual third order Jacobsthal quaternions, Proyecciones Journal of Mathematics, 37(4), (2018), 731-747.
4. Cerda-Morales, G., New identities for Padovan numbers, arXiv.org, (2019). https://arxiv.org/abs/1904.05492
5. Cerda-Morales, G., On a generalization for Tribonacci quaternions, Mediterr. J. Math., 14(6), Article number: 239 (2017), 12 pages.