Geodesic
Two-sided estimates of the central binomial coefficient
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 1, pp. 56-69

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The previous two-sided estimates of the central binomial coefficient are strengthened. The established boundaries are sufficiently exact. They act immediately on the sequence $C_ {2n} ^ n$ for all numbers $n\in\mathbb{N}$. The results can be used in mathematical analysis, combinatorics and probability theory.
Keywords: combinatorial values, central binomial coefficient, two-sided estimates, asymptotic expansion, enveloping series. 
@article{CHFMJ_2020_5_1_a4,
     author = {A. Yu. Popov},
     title = {Two-sided estimates of the central binomial coefficient},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {56--69},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_1_a4/}
}
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A. Yu. Popov. Two-sided estimates of the central binomial coefficient. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 1, pp. 56-69. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_1_a4/