{"title":"保利-莱昂纳多四元数","authors":"Zehra İşbilir, M. Akyiğit, M. Tosun","doi":"10.7546/nntdm.2023.29.1.1-16","DOIUrl":null,"url":null,"abstract":"In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities, and the sum properties of these novel quaternions. In addition, we investigate the interrelations between Pauli–Leonardo quaternions and the Pauli–Fibonacci, Pauli–Lucas quaternions. Moreover, we create some algorithms that determine the terms of the Pauli–Leonardo quaternions. Finally, we generate the matrix representations of the Pauli–Leonardo quaternions and ℝ-linear transformations.","PeriodicalId":44060,"journal":{"name":"Notes on Number Theory and Discrete Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Pauli–Leonardo quaternions\",\"authors\":\"Zehra İşbilir, M. Akyiğit, M. Tosun\",\"doi\":\"10.7546/nntdm.2023.29.1.1-16\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities, and the sum properties of these novel quaternions. In addition, we investigate the interrelations between Pauli–Leonardo quaternions and the Pauli–Fibonacci, Pauli–Lucas quaternions. Moreover, we create some algorithms that determine the terms of the Pauli–Leonardo quaternions. Finally, we generate the matrix representations of the Pauli–Leonardo quaternions and ℝ-linear transformations.\",\"PeriodicalId\":44060,\"journal\":{\"name\":\"Notes on Number Theory and Discrete Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-01-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Notes on Number Theory and Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7546/nntdm.2023.29.1.1-16\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Notes on Number Theory and Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7546/nntdm.2023.29.1.1-16","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities, and the sum properties of these novel quaternions. In addition, we investigate the interrelations between Pauli–Leonardo quaternions and the Pauli–Fibonacci, Pauli–Lucas quaternions. Moreover, we create some algorithms that determine the terms of the Pauli–Leonardo quaternions. Finally, we generate the matrix representations of the Pauli–Leonardo quaternions and ℝ-linear transformations.
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