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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2020, Volume 5, Issue 1, Pages 70–95
DOI: https://doi.org/10.24411/2500-0101-2020-15106 (Mi chfmj169) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

Comparative analysis of two-sided estimates of the central binomial coefficient

I. V. Tikhonova, V. B. Sherstyukovb, D. G. Tsvetkovichc

a Lomonosov Moscow State University, Moscow, Russia
b National Research Nuclear University MEPhI, Moscow, Russia
c Moscow Pedagogical State University, Moscow, Russia
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DOI: https://doi.org/10.24411/2500-0101-2020-15106
Abstract: A numerical analysis of two-sided estimates of the central binomial coefficient and some special quotients of the gamma function is presented. We give detailed calculation tables and compare the quality of several possible estimates with each other. The results illustrate, in particular, the analytical study of A.Yu. Popov, which is published in the same issue of the "Chelyabinsk Physical and Mathematical Journal" . Theoretical and historical information is provided. In addition, an elementary proof of some estimate with optimal choice of parameters is proposed.
Keywords: central binomial coefficient, the gamma function, two-sided estimates, continued fractions, systems of computer mathematics.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00236_a
Received: 30.01.2020
Revised: 02.03.2020
Document Type: Article
UDC: 517.521.1+517.581+519.114
Language: Russian
Citation: I. V. Tikhonov, V. B. Sherstyukov, D. G. Tsvetkovich, “Comparative analysis of two-sided estimates of the central binomial coefficient”, Chelyab. Fiz.-Mat. Zh., 5:1 (2020), 70–95
Citation in format AMSBIB
\Bibitem{TikSheTsv20}
\by I.~V.~Tikhonov, V.~B.~Sherstyukov, D.~G.~Tsvetkovich
\paper Comparative analysis of two-sided estimates of the central binomial coefficient
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2020
\vol 5
\issue 1
\pages 70--95
\mathnet{http://mi.mathnet.ru/chfmj169}
\crossref{https://doi.org/10.24411/2500-0101-2020-15106}
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