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Among various approximation formulas for the gamma function, Smith showed that Γ(x+12)∼S(x)=2π(xe)x(2xtanh12x)x/2,x→∞, which is a little-known but accurate and simple one. In this note, we prove that the function x↦lnΓ(x+1/2)−lnS(x) is strictly increasing and concave on (0,∞), which shows that Smith’s approximation is just an upper one. [ABSTRACT FROM AUTHOR]