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

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.