On hypercomplex numbers with third-order $k$-Jacobsthal numbers
Year: 2025
Type: article
Abstract: UDC 517.5 We introduce a new family of hypercomplex numbers by using third-order $k$-Jacobsthal numbers. These sequences are called the third-order $k$-Jacobsthal $2^{r}$-ions. We present some algebraic properties of the third order $k$-Jacobsthal $2^{r}$-ions, such as the recurrence relation, the Binet formula, generating function, exponential generation function, the d'Ocagne identity, and the Cassini identity. Further, we obtain the matrix representation of the third-order $k$-Jacobsthal $2^{r}$-ions.
Author: Gamaliel Morales
Institution: Pontificia Universidad Católica de Valparaíso
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7084081739
FWCI:
Cites:
Cited by:
Related to: