On expansions of numbers in alternating <Emphasis Type="Italic">s</Emphasis>-adic series and Ostrogradskii series of the first and second kind |
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| Authors: | I M Prats’ovyta |
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| Institution: | (1) Department of Nuclear Medicine, University Medical Center Nijmegen (565), 9101, 6500 Nijmegen, The Netherlands;(2) Department of Radiology, University Medical Center Nijmegen, Nijmegen, The Netherlands |
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| Abstract: | 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 structure and metric-topological and fractal properties of the distribution
of the random variable
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x = \frac1st1 - 1 + ?k = 2￥ \frac( - 1 )k - 1st1 + t2 + ... + tk - 1, {\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}},} |
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