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

  • I. M. Prats’ovyta
We present expansions of real numbers in alternating s-adic series (1 < sN), 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 structure and metric-topological and fractal properties of the distribution of the random variable
$$ {\xi } = \frac{1}{s^{{\tau_1} - 1}} + \sum\limits_{k = 2}^\infty {\frac{{\left( { - 1} \right)}^{k - 1}}{s^{{\tau_1} + {\tau_2} + ... + {\tau_k} - 1}},} $$
where τ k are independent random variables that take natural values.


Fractal Property Independent Random Variable Absolute Continuity Irrational Number Infinite Product 
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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • I. M. Prats’ovyta
    • 1
  1. 1.National Pedagogic UniversityKyivUkraine

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