Abstract
<abstract><p>This paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented. In addition, a new dual vector called the dual Jacobsthal vector is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of dual space. Finally, this study introduces the dual Jacobsthal and the dual Jacobsthal-Lucas numbers with coefficients of dual numbers. Some fundamental identities are demonstrated, such as the generating function, the Binet formulas, the Cassini's, Catalan's and d'Ocagne identities for these numbers.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference12 articles.
1. H. W. Guggenheimer, Differential geometry, McGraw-Hill, New York, 1963.
2. E. Study, Geometry der dynamen, Leipzig, 1901.
3. S. Aslan, Kinematic applications of hyper-dual numbers, Int. Electron. J. Geom., 14 (2021), 292–304. https://doi.org/10.36890/iejg.888373
4. S. K. Nurkan, I. A. Guven, A new approach to Fibonacci, Lucas numbers and dual vectors, Adv. Appl. Clifford Al., 25 (2015), 577–590. https://doi.org/10.1007/s00006-014-0516-7
5. A. F. Horadam, Jacobsthal representation numbers, Fibonacci Quart., 34 (1996), 40–54. https://doi.org/10.2307/4613247