{"title":"各种幂和的表示方法","authors":"Bikash Chakraborty, Raymond Mortini","doi":"10.1007/s00025-024-02190-8","DOIUrl":null,"url":null,"abstract":"<p>We give new representations of various power sums, including the signed/alternating sum of powers of consecutive integers as well as odd numbers. The generalized Eulerian power sums <span>\\(E_{n,m}(z):=\\sum _{k=1}^n k^mz^k\\)</span> are also considered.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Representations of Various Power Sums\",\"authors\":\"Bikash Chakraborty, Raymond Mortini\",\"doi\":\"10.1007/s00025-024-02190-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give new representations of various power sums, including the signed/alternating sum of powers of consecutive integers as well as odd numbers. The generalized Eulerian power sums <span>\\\\(E_{n,m}(z):=\\\\sum _{k=1}^n k^mz^k\\\\)</span> are also considered.</p>\",\"PeriodicalId\":54490,\"journal\":{\"name\":\"Results in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00025-024-02190-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00025-024-02190-8","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We give new representations of various power sums, including the signed/alternating sum of powers of consecutive integers as well as odd numbers. The generalized Eulerian power sums \(E_{n,m}(z):=\sum _{k=1}^n k^mz^k\) are also considered.
期刊介绍:
Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.