{"title":"坎特椭圆作为与三角函数有关的数列的子集","authors":"M. Pratsiovytyi, Dmytro Karvatskyi","doi":"10.15673/pigc.v16i3.2519","DOIUrl":null,"url":null,"abstract":"We study properties of the set of subsums for convergent series k1 sin x + ... + km sin x + ... + k1 sin x[(n-1)/m+1] + ... + km sin x[(n-1)/m+1] + ... where k1, k2, k3, ..., km are fixed positive integers and 0<x<1. It is proved that depending on the parameter x this set can be a finite union of closed intervals or Cantor-type set or even Cantorval.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cantorvals as sets of subsums for a series connected with trigonometric functions\",\"authors\":\"M. Pratsiovytyi, Dmytro Karvatskyi\",\"doi\":\"10.15673/pigc.v16i3.2519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study properties of the set of subsums for convergent series k1 sin x + ... + km sin x + ... + k1 sin x[(n-1)/m+1] + ... + km sin x[(n-1)/m+1] + ... where k1, k2, k3, ..., km are fixed positive integers and 0<x<1. It is proved that depending on the parameter x this set can be a finite union of closed intervals or Cantor-type set or even Cantorval.\",\"PeriodicalId\":36547,\"journal\":{\"name\":\"Proceedings of the International Geometry Center\",\"volume\":\"13 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the International Geometry Center\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15673/pigc.v16i3.2519\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the International Geometry Center","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15673/pigc.v16i3.2519","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
我们研究收敛级数 k1 sin x + ...+ km sin x + ...+ k1 sin x[(n-1)/m+1] + ...+ km sin x[(n-1)/m+1] + ... 其中 k1、k2、k3、...、km 为固定的正整数,0本文章由计算机程序翻译,如有差异,请以英文原文为准。
Cantorvals as sets of subsums for a series connected with trigonometric functions
We study properties of the set of subsums for convergent series k1 sin x + ... + km sin x + ... + k1 sin x[(n-1)/m+1] + ... + km sin x[(n-1)/m+1] + ... where k1, k2, k3, ..., km are fixed positive integers and 0