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...
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Lugansk National Taras Shevchenko University
2017
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2017-10-11T02:10:07Z |
| collection |
OJS |
| language |
English |
| topic |
Jacobsthal-Lucas sequence set of incomplete sums singular random variable Hausdorff-Besicovitch dimension 11B83 11B39 60G50 |
| 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 |
| topic_facet |
Jacobsthal-Lucas sequence set of incomplete sums singular random variable Hausdorff-Besicovitch dimension 11B83 11B39 60G50 |
| format |
Article |
| author |
Pratsiovytyi, Mykola Karvatsky, Dmitriy |
| author_facet |
Pratsiovytyi, Mykola Karvatsky, Dmitriy |
| author_sort |
Pratsiovytyi, Mykola |
| title |
Jacobsthal-Lucas series and their applications |
| title_short |
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_sort |
jacobsthal-lucas series and their applications |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2017 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/297 |
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AT pratsiovytyimykola jacobsthallucasseriesandtheirapplications AT karvatskydmitriy jacobsthallucasseriesandtheirapplications |
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2025-07-17T10:33:40Z |
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2025-07-17T10:33:40Z |
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1837889928494579712 |