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Mat. Zametki, 2015, Volume 97, Issue 4, Pages 483–492 (Mi mz10201)  

This article is cited in 1 scientific paper (total in 1 paper)

Symmetrized Version of the Markovecchio Integral in the Theory of Diophantine Approximations

V. A. Androsenko, V. Kh. Salikhova

a Bryansk State Technical University

Abstract: A new integral construction unifying the idea of symmetry proposed by Salikhov in 2007 and the integral introduced by Markovecchio in 2009 is considered. The application of this construction leads, in particular, to a sharper estimate of the measure of irrationality of the number $\pi/\sqrt{3}$.

Keywords: Diophantine approximation, Markovecchio integral, Salikhov symmetrized integral, measure of irrationality, Gauss hypergeometric function, Kummer's formula.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00171
This work was supported by the Russian Foundation for Basic Research (grant no. 12-01-00171).


DOI: https://doi.org/10.4213/mzm10201

Full text: PDF file (450 kB)
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English version:
Mathematical Notes, 2015, 97:4, 493–501

Bibliographic databases:

Document Type: Article
UDC: 511.36
Received: 01.11.2012
Revised: 01.02.2013

Citation: V. A. Androsenko, V. Kh. Salikhov, “Symmetrized Version of the Markovecchio Integral in the Theory of Diophantine Approximations”, Mat. Zametki, 97:4 (2015), 483–492; Math. Notes, 97:4 (2015), 493–501

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Yu. Luchin, V. Kh. Salikhov, “Approximating $\ln 2$ by numbers in the field $\mathbb{Q}(\sqrt{2} )$”, Izv. Math., 82:3 (2018), 549–577  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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