{"title":"类维塔-斐波那契多项式和一些恒等式","authors":"Wanna Sriprad, Somnuk Srisawat, Peesiri Naklor","doi":"10.33039/ami.2021.09.002","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a new type of the Vieta polynomial, which is Vieta–Fibonacci-like polynomial. After that, we establish the Binet formula, the generating function, the well-known identities, and the sum formula of this polynomial. Finally, we present the relationship between this polynomial and the previous well-known Vieta polynomials.","PeriodicalId":43454,"journal":{"name":"Annales Mathematicae et Informaticae","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Vieta–Fibonacci-like polynomials and some identities\",\"authors\":\"Wanna Sriprad, Somnuk Srisawat, Peesiri Naklor\",\"doi\":\"10.33039/ami.2021.09.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce a new type of the Vieta polynomial, which is Vieta–Fibonacci-like polynomial. After that, we establish the Binet formula, the generating function, the well-known identities, and the sum formula of this polynomial. Finally, we present the relationship between this polynomial and the previous well-known Vieta polynomials.\",\"PeriodicalId\":43454,\"journal\":{\"name\":\"Annales Mathematicae et Informaticae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Mathematicae et Informaticae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33039/ami.2021.09.002\",\"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":"Annales Mathematicae et Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33039/ami.2021.09.002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Vieta–Fibonacci-like polynomials and some identities
In this paper, we introduce a new type of the Vieta polynomial, which is Vieta–Fibonacci-like polynomial. After that, we establish the Binet formula, the generating function, the well-known identities, and the sum formula of this polynomial. Finally, we present the relationship between this polynomial and the previous well-known Vieta polynomials.
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