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SUMMARY:Mykola Moroz (Institute of Mathematics\, Natl. Acad. Sci. Ukraine)
DTSTART:20250213T133000Z
DTEND:20250213T150000Z
DTSTAMP:20260423T024558Z
UID:fran/62
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/62/">Re
 presentation of real numbers by alternating Perron series and its metric e
 quivalence to representation of numbers by positive Perron series</a>\nby 
 Mykola Moroz (Institute of Mathematics\, Natl. Acad. Sci. Ukraine) as part
  of Семінар з фрактального аналізу / Fractal an
 alysis seminar\n\n\nAbstract\nIn this talk\, we consider the representatio
 n of real numbers by alternating Perron series (an analog of positive Perr
 on series)\, which generalizes expansions of numbers in alternating Lürot
 h series\, Ostrogradsky–Sierpiński–Pierce series\, second Ostrogradsk
 y series\, etc. The main result is a metric equivalence of representations
  of numbers by positive and alternating Perron series. This equivalence ex
 plains analogies in the individual theories of representations of numbers 
 by various positive and alternating series on a basic level. The series ar
 e the following: positive and alternating Lüroth series\, modified Engel 
 series and Ostrogradsky–Sierpiński–Pierce series\, Sylvester series a
 nd second Ostrogradsky series. We also analyze the known “identical” r
 esults\, which are explained by the discovered metric equivalence.\n
LOCATION:https://researchseminars.org/talk/fran/62/
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