Jacobsthal-Lucas series and their applications
In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence (\(J_{n+2}=2J_{n+1}+J_n\), \(J_1=2\), \(J_2=1\)). In particular, we consider the properties of the set of incomplete sums as well as their applications. We prove...
Збережено в:
| Дата: | 2017 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2017
|
| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/297 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543391633899520 |
|---|---|
| author | Pratsiovytyi, Mykola Karvatsky, Dmitriy |
| author_facet | Pratsiovytyi, Mykola Karvatsky, Dmitriy |
| author_sort | Pratsiovytyi, Mykola |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-10-11T02:10:07Z |
| description | In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence (\(J_{n+2}=2J_{n+1}+J_n\), \(J_1=2\), \(J_2=1\)). In particular, we consider the properties of the set of incomplete sums as well as their applications. We prove that the set of incomplete sums of this series is a nowhere dense set of positive Lebesgue measure. Also we study singular random variables of Cantor type related to Jacobsthal-Lucas sequence. |
| first_indexed | 2025-12-02T15:42:45Z |
| format | Article |
| id | admjournalluguniveduua-article-297 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:42:45Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-2972017-10-11T02:10:07Z Jacobsthal-Lucas series and their applications Pratsiovytyi, Mykola Karvatsky, Dmitriy Jacobsthal-Lucas sequence, set of incomplete sums, singular random variable, Hausdorff-Besicovitch dimension 11B83, 11B39, 60G50 In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence (\(J_{n+2}=2J_{n+1}+J_n\), \(J_1=2\), \(J_2=1\)). In particular, we consider the properties of the set of incomplete sums as well as their applications. We prove that the set of incomplete sums of this series is a nowhere dense set of positive Lebesgue measure. Also we study singular random variables of Cantor type related to Jacobsthal-Lucas sequence. Lugansk National Taras Shevchenko University 2017-10-07 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/297 Algebra and Discrete Mathematics; Vol 24, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/297/pdf Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | Jacobsthal-Lucas sequence set of incomplete sums singular random variable Hausdorff-Besicovitch dimension 11B83 11B39 60G50 Pratsiovytyi, Mykola Karvatsky, Dmitriy Jacobsthal-Lucas series and their applications |
| title | Jacobsthal-Lucas series and their applications |
| title_full | Jacobsthal-Lucas series and their applications |
| title_fullStr | Jacobsthal-Lucas series and their applications |
| title_full_unstemmed | Jacobsthal-Lucas series and their applications |
| title_short | Jacobsthal-Lucas series and their applications |
| title_sort | jacobsthal-lucas series and their applications |
| topic | Jacobsthal-Lucas sequence set of incomplete sums singular random variable Hausdorff-Besicovitch dimension 11B83 11B39 60G50 |
| topic_facet | Jacobsthal-Lucas sequence set of incomplete sums singular random variable Hausdorff-Besicovitch dimension 11B83 11B39 60G50 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/297 |
| work_keys_str_mv | AT pratsiovytyimykola jacobsthallucasseriesandtheirapplications AT karvatskydmitriy jacobsthallucasseriesandtheirapplications |