  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.
