On hypercomplex numbers with third-order $k$-Jacobsthal numbers
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 B...
Gespeichert in:
| Datum: | 2026 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8969 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
|---|---|
| DOI: | 10.3842/umzh.v77i10.8969 |