On expansions of numbers in alternating s-adic series and Ostrogradskii series of the first and second kind

• Datum: 2009
• Hauptverfasser: Prats’ovyta, I. M., Працьовита, I. М.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2009
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3070
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We present expansions of real numbers in alternating $s$-adic series $(1 < s ∈ N)$, in particular, $s$-adic Ostrogradskii series of the first and second kind. We study the “geometry” of this representation of numbers and solve metric and probability problems, including the problem of structur...