{"title":"拆分对偶雅各布斯塔尔和雅各布斯塔尔-卢卡斯四元数","authors":"Umit Tokeser, Zafer Unal","doi":"10.56557/ajomcor/2022/v29i37938","DOIUrl":null,"url":null,"abstract":"Many researchs have been studied on quaternions since Hamilton introduced them to the literature in 1843. In our paper, we gave split dual Jacobsthal (SDJ) and split dual Jacobsthal-Lucas (SDJL) quaternions over the algebra H(μ,n) with the basis {1; e1; e2; e3}, where μ,n ∈ Z. Binet like formulaes are obtained for these quaternions. Also, given Vajda identities for SDJ and SDJL quaternions.As a special case of Vajda identities, d'Ocagne's, Cassini's and Catalan's identities are represented.","PeriodicalId":200824,"journal":{"name":"Asian Journal of Mathematics and Computer Research","volume":"76 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SPLIT DUAL JACOBSTHAL AND JACOBSTHAL-LUCAS QUATERNIONS\",\"authors\":\"Umit Tokeser, Zafer Unal\",\"doi\":\"10.56557/ajomcor/2022/v29i37938\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many researchs have been studied on quaternions since Hamilton introduced them to the literature in 1843. In our paper, we gave split dual Jacobsthal (SDJ) and split dual Jacobsthal-Lucas (SDJL) quaternions over the algebra H(μ,n) with the basis {1; e1; e2; e3}, where μ,n ∈ Z. Binet like formulaes are obtained for these quaternions. Also, given Vajda identities for SDJ and SDJL quaternions.As a special case of Vajda identities, d'Ocagne's, Cassini's and Catalan's identities are represented.\",\"PeriodicalId\":200824,\"journal\":{\"name\":\"Asian Journal of Mathematics and Computer Research\",\"volume\":\"76 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Journal of Mathematics and Computer Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56557/ajomcor/2022/v29i37938\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics and Computer Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56557/ajomcor/2022/v29i37938","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SPLIT DUAL JACOBSTHAL AND JACOBSTHAL-LUCAS QUATERNIONS
Many researchs have been studied on quaternions since Hamilton introduced them to the literature in 1843. In our paper, we gave split dual Jacobsthal (SDJ) and split dual Jacobsthal-Lucas (SDJL) quaternions over the algebra H(μ,n) with the basis {1; e1; e2; e3}, where μ,n ∈ Z. Binet like formulaes are obtained for these quaternions. Also, given Vajda identities for SDJ and SDJL quaternions.As a special case of Vajda identities, d'Ocagne's, Cassini's and Catalan's identities are represented.
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