{"title":"关于具有广义Fibonacci和Lucas数系数的双复数","authors":"A. Cihan, A. Z. Azak, M. Güngör","doi":"10.36753/mathenot.621602","DOIUrl":null,"url":null,"abstract":"In this paper, dual-complex Fibonacci numbers with generalized Fi bonacci and Lucas coefficients are dened. Generating function is given for this number system. Binet formula is obtained by the help of this generat ing function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger, Tagiuri and other identities are given for this number system. Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].","PeriodicalId":127589,"journal":{"name":"Mathematical Sciences and Applications E-Notes","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients\",\"authors\":\"A. Cihan, A. Z. Azak, M. Güngör\",\"doi\":\"10.36753/mathenot.621602\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, dual-complex Fibonacci numbers with generalized Fi bonacci and Lucas coefficients are dened. Generating function is given for this number system. Binet formula is obtained by the help of this generat ing function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger, Tagiuri and other identities are given for this number system. Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].\",\"PeriodicalId\":127589,\"journal\":{\"name\":\"Mathematical Sciences and Applications E-Notes\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Sciences and Applications E-Notes\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.36753/mathenot.621602\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Sciences and Applications E-Notes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.36753/mathenot.621602","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients
In this paper, dual-complex Fibonacci numbers with generalized Fi bonacci and Lucas coefficients are dened. Generating function is given for this number system. Binet formula is obtained by the help of this generat ing function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger, Tagiuri and other identities are given for this number system. Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].
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