Numerical characteristics of the random variable associated with the expansions of real numbers by the Engel series

• Date: 2020
• Main Authors: Moroz, M. P., М. П., Мороз, М. П.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2284
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

It is known that any $x \in \left(0;1\right]\equiv\Omega$ has a unique Engel expansion $$ \displaystyle x=\sum\limits_{n=1}^{\infty}\frac{1}{\left(p_1(x)+1\right)\ldots \left(p_n(x)+1\right)},$$ where $p_n(x)\in\mathbb{N},$ $p_{n+1}(x)\geq p_n(x)$ for all $n \i...