Gauss–Kuzmin problem for the difference Engel-series representation of real numbers

• Date: 2022
• Main Authors: Moroz , M. P., Мороз, М. П.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7159
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 511.7+517.5 Let $x=\Delta^{\overline{E}}_{g_1(x)\ldots g_n(x)\ldots}$ be the difference Engel-series representation of a real number $x\in\left(0;1\right]$ (${\overline{E}}$-representation), where $\Delta^{\overline{E}}_{g_1\ldots g_n\ldots}=\displaystyle\sum\nolimits_{n=1}^\infty\dfrac{1}{(2+g_...