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Asymptotic approximation of central binomial coefficients with rigorous error bounds
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abstract
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.
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The mean absolute deviation of the classical discrete distributions: collapse identities, complete asymptotic expansions, and enveloping series
A common telescoping identity yields closed forms, complete asymptotics, and enveloping series for the mean absolute deviation of the four classical discrete laws.
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