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<x<1. It is proved that depending on the parameter x this set can be a finite union...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2023-12-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2519 |
| _version_ | 1797390239955681280 |
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| author | Mykola Pratsiovytyi Dmytro Karvatskyi |
| author_facet | Mykola Pratsiovytyi Dmytro Karvatskyi |
| author_sort | Mykola Pratsiovytyi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T23:08:54Z |
| format | Article |
| id | doaj.art-c496fac1777f4bd780ad027a63b10559 |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-03-08T23:08:54Z |
| publishDate | 2023-12-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-c496fac1777f4bd780ad027a63b105592023-12-15T10:27:48ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062023-12-01163-426227110.15673/pigc.v16i3.25192519Cantorvals as sets of subsums for a series connected with trigonometric functionsMykola Pratsiovytyi0Dmytro Karvatskyi1Institute of Mathematics of NAS of UkraineInstitute of Mathematics of NAS of UkraineWe 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.https://journals.ontu.edu.ua/index.php/geometry/article/view/2519achievement set of sequencemultigeometric seriesthe set of subsumscantorval |
| spellingShingle | Mykola Pratsiovytyi Dmytro Karvatskyi Cantorvals as sets of subsums for a series connected with trigonometric functions Pracì Mìžnarodnogo Geometričnogo Centru achievement set of sequence multigeometric series the set of subsums cantorval |
| title | Cantorvals as sets of subsums for a series connected with trigonometric functions |
| title_full | Cantorvals as sets of subsums for a series connected with trigonometric functions |
| title_fullStr | Cantorvals as sets of subsums for a series connected with trigonometric functions |
| title_full_unstemmed | Cantorvals as sets of subsums for a series connected with trigonometric functions |
| title_short | Cantorvals as sets of subsums for a series connected with trigonometric functions |
| title_sort | cantorvals as sets of subsums for a series connected with trigonometric functions |
| topic | achievement set of sequence multigeometric series the set of subsums cantorval |
| url | https://journals.ontu.edu.ua/index.php/geometry/article/view/2519 |
| work_keys_str_mv | AT mykolapratsiovytyi cantorvalsassetsofsubsumsforaseriesconnectedwithtrigonometricfunctions AT dmytrokarvatskyi cantorvalsassetsofsubsumsforaseriesconnectedwithtrigonometricfunctions |