{"title":"通过卡西尼公式计算佩尔和佩尔-卢卡斯多项式的反正切数列","authors":"Dongwei Guo, Wenchang Chu","doi":"10.61091/um118-01","DOIUrl":null,"url":null,"abstract":"By combining the telescoping method with Cassini–like formulae, we evaluate, in closed forms, four classes of sums about products of two arctangent functions with their argument involving Pell and Pell–Lucas polynomials. Several infinite series identities for Fibonacci and Lucas numbers are deduced as consequences.","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"85 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Arctangent Series on Pell and Pell-Lucas Polynomials via Cassini-Like Formulae\",\"authors\":\"Dongwei Guo, Wenchang Chu\",\"doi\":\"10.61091/um118-01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"By combining the telescoping method with Cassini–like formulae, we evaluate, in closed forms, four classes of sums about products of two arctangent functions with their argument involving Pell and Pell–Lucas polynomials. Several infinite series identities for Fibonacci and Lucas numbers are deduced as consequences.\",\"PeriodicalId\":49389,\"journal\":{\"name\":\"Utilitas Mathematica\",\"volume\":\"85 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Utilitas Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.61091/um118-01\",\"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":"Utilitas Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.61091/um118-01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Arctangent Series on Pell and Pell-Lucas Polynomials via Cassini-Like Formulae
By combining the telescoping method with Cassini–like formulae, we evaluate, in closed forms, four classes of sums about products of two arctangent functions with their argument involving Pell and Pell–Lucas polynomials. Several infinite series identities for Fibonacci and Lucas numbers are deduced as consequences.
期刊介绍：
Utilitas Mathematica publishes papers in all areas of statistical designs and combinatorial mathematics, including graph theory, design theory, extremal combinatorics, enumeration, algebraic combinatorics, combinatorial optimization, Ramsey theory, automorphism groups, coding theory, finite geometries, chemical graph theory, etc., as well as the closely related area of number-theoretic polynomials for enumeration.
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