{"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}
引用次数: 0
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
