Sum and weighted sum formulas for fibonacci and lucas quaternions
| dc.authorid | 0000-0003-3652-5354 | |
| dc.contributor.author | Karataş, Adnan | |
| dc.date.accessioned | 2025-01-30T08:02:25Z | |
| dc.date.available | 2025-01-30T08:02:25Z | |
| dc.date.issued | 2024 | |
| dc.department | Sabire Yazıcı Fen Edebiyat Fakültesi | |
| dc.description.abstract | Fibonacci and Lucas quaternions are deeply studied in the literature after its definition by Horadam in 1963. Binet formula, generation function, Cassini, Catalan, Honsberger, and other identities for these sequences studied in different quaternion algebra types like split quaternion algebra, dual quaternion algebra, etc. Additionally, some of the generalizations for Fibonacci and Lucas quaternions are studied like k-Fibonacci quaternions, k-Lucas quaternions, Horadam quaternions, and more. However, despite being researched intensively, the summation formulas or weighted summation formulas for these sequences are not examined thoroughly. In this study, after briefly summarizing the literature, we focused on the summation and the weighted summation formulas for the Fibonacci and the Lucas quaternions. In addition, we provided generalized weighted summation formulas for the Fibonacci and Lucas quaternions. Moreover, we calculated generalized weighted summation formulas for the double coefficient Fibonacci and double coefficient Lucas quaternions which have two Fibonacci and Lucas coefficient in every unit of the quaternion, respectively. | |
| dc.identifier.doi | 10.29002/asujse.1576933 | |
| dc.identifier.endpage | 121 | en_US |
| dc.identifier.issn | 2587-1277 | |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.startpage | 114 | en_US |
| dc.identifier.uri | https://doi.org/10.29002/asujse.1576933 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12451/12846 | |
| dc.identifier.volume | 8 | en_US |
| dc.language.iso | en | |
| dc.publisher | Aksaray Üniversitesi | |
| dc.relation.ispartof | Aksaray University Journal of Science and Engineering (ASUJSE) | |
| dc.relation.publicationcategory | Konferans Öğesi - Uluslararası - Başka Kurum Yazarı | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.subject | Fibonacci Numbers | |
| dc.subject | Lucas Numbers | |
| dc.subject | Sum Formulas | |
| dc.subject | Weighted Sum Formulas | |
| dc.subject | Double Coefficient Fibonacci Numbers | |
| dc.title | Sum and weighted sum formulas for fibonacci and lucas quaternions | |
| dc.type | Article |
