Jacobsthal-Lucas series and their applications

• Date: 2017
• Main Authors: Pratsiovytyi, Mykola, Karvatsky, Dmitriy
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: Jacobsthal-Lucas sequence; set of incomplete sums; singular random variable; Hausdorff-Besicovitch dimension; 11B83; 11B39; 60G50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/297
• Journal Title: Algebra and Discrete Mathematics

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...