中心二项式系数具有严格误差界的渐近逼近
Asymptotic approximation of central binomial coefficients with rigorous error bounds
摘要：
我们证明了一个著名的中心二项式系数的对数的渐近级数在Pólya和Szegö意义下是严格包络的，因此截断该级数所产生的误差与下一项的符号相同，并且在幅度上受该项的限制。我们考虑了比奈函数、$\lnΓ(z+1/2)$和Riemann-Siegel θ函数的密切相关的渐近级数，并作了一些历史性的评论。
英文摘要：
We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of Pólya and Szegö, 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 $\lnΓ(z+1/2)$, and for the Riemann-Siegel theta function, and make some historical remarks.
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