We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of P\'olya and Szeg\"o, so the error incurred in truncating the series is of the same sign as the next term, and is bounded in magnitude by that term. We consider closely related asymptotic series for Binet's function, for $\ln\Gamma(z+1/2)$, and for the Riemann-Siegel theta function, and make some historical remarks.

翻译：我们显示,一个众所周知的中央二元系数对数的无症状序列严格地包含在 P\'olya 和 Szeg\\"o 的意义上,因此,在缩短序列时发生的错误与下一个术语的符号相同,并且与该术语的大小相连接。 我们考虑将Binet 函数、 $\ln\ Gamma (z+1/2) 和 Riemann- Siegel theta 函数紧密相连的无症状序列, 并发表一些历史评论 。