Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Nesterenko A. Y. Parameters Recovering Algorithm for One Class of Irrationalities. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 89-93. DOI: 10.18500/1816-9791-2013-13-4-89-93

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
25.11.2013
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Russian
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UDC: 
511.4

Parameters Recovering Algorithm for One Class of Irrationalities

Autors: 
Nesterenko Alexey Yur'evich, National Research University of Electronic Technology, Russia
Abstract: 

In this article we study one class of irrationalities whichmay be defined as covergent series with rational coefficients. This class contain a lot of well known constants such as ln 2, ¼, e.t.c. We consider the problem of determination parameters of rational coefficients by rational approximation of irrationality. We deduced the lower and upper bounds and present an algorithm for determination of unknown parameters. Also, we present some results of practical calculations.

References: 
  1. Bayley D. H. A Compendium of BBP-type Formulas for Mathematical Constants. Preprint. April, 2013. Available at: http://crd.lbl.gov/˜dhbailey/dhbpapers/bbpformulas.pdf (Accessed 10, September, 2013).
  2. Nesterenko A. Yu. On the statistical properties of some transcendetal numbers. Uchenye zapiski Orlovskogo gosudarstvennogo universiteta [Scientific notes of the Oryol State University], 2012, no. 6, pt. 2, pp. 170–176 (in Russian).
  3. Ferguson H. R. P., Bailey D. H., Arno S. Analysis of PSLQ, An Integer Relation Finding Algorithm. Mathematics of Computation, 1999, vol. 68, no. 225, pp. 351–369.
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