{"title":"On Quaternions with Higher Order Jacobsthal Numbers Components","authors":"Engin ÖZKAN, Mine UYSAL","doi":"10.35378/gujs.1002454","DOIUrl":null,"url":null,"abstract":"In this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions.","PeriodicalId":12615,"journal":{"name":"gazi university journal of science","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"gazi university journal of science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35378/gujs.1002454","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 1
Abstract
In this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions.
期刊介绍：
The scope of the “Gazi University Journal of Science” comprises such as original research on all aspects of basic science, engineering and technology. Original research results, scientific reviews and short communication notes in various fields of science and technology are considered for publication. The publication language of the journal is English. Manuscripts previously published in another journal are not accepted. Manuscripts with a suitable balance of practice and theory are preferred. A review article is expected to give in-depth information and satisfying evaluation of a specific scientific or technologic subject, supported with an extensive list of sources. Short communication notes prepared by researchers who would like to share the first outcomes of their on-going, original research work are welcome.
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