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Mat. Zametki, 2010, Volume 88, Issue 4, Pages 583–593 (Mi mz8688)  

This article is cited in 6 scientific papers (total in 6 papers)

On the Measure of Irrationality of the Number $\pi$

V. Kh. Salikhov

Bryansk State Technical University

Abstract: A new estimate of the measure of irrationality of the number $\pi$ is obtained. The previous result (M. Hata, 1993) is improved by means of another integral construction.

Keywords: measure of irrationality, approximation by rational fractions, partial-fraction expansion, Leibniz formula, linear form

DOI: https://doi.org/10.4213/mzm8688

Full text: PDF file (493 kB)
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English version:
Mathematical Notes, 2010, 88:4, 563–573

Bibliographic databases:

UDC: 511.36
Received: 25.11.2009

Citation: V. Kh. Salikhov, “On the Measure of Irrationality of the Number $\pi$”, Mat. Zametki, 88:4 (2010), 583–593; Math. Notes, 88:4 (2010), 563–573

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, “Otsenka mery irratsionalnosti chisla $\ln\frac74$”, Chebyshevskii sb., 14:2 (2013), 123–131  mathnet
    2. M. Yu. Luchin, “Otsenka mery irratsionalnosti chisla $\log \frac{37}{30} $”, Chebyshevskii sb., 15:1 (2014), 131–140  mathnet
    3. V. A. Androsenko, “Irrationality measure of the number $\frac{\pi}{\sqrt{3}}$”, Izv. Math., 79:1 (2015), 1–17  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. A. Androsenko, V. Kh. Salikhov, “Symmetrized Version of the Markovecchio Integral in the Theory of Diophantine Approximations”, Math. Notes, 97:4 (2015), 493–501  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. I. V. Bondareva, M. Yu. Luchin, V. Kh. Salikhov, “Simmetrizovannye mnogochleny v zadache otsenki mery irratsionalnosti chisla $\ln 3$”, Chebyshevskii sb., 19:1 (2018), 15–25  mathnet  crossref  elib
    6. A. V. Begunts, “On the Convergence of Alternating Series Associated with Beatty Sequences”, Math. Notes, 107:2 (2020), 345–349  mathnet  crossref  crossref  isi  elib
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