The correction θ(x) in XXXXXXXXXXfor Stirling’s formula has the series expansion where the higher terms (not needed for this exercise) involve Bernoulli numbers Bk. Computing a least maximum...

The correction θ(x) in (7.6.2) for Stirling’s formula has the series expansion

where the higher terms (not needed for this exercise) involve Bernoulli numbers Bk. Computing a least maximum approximation on an infinite interval such as [8,∞] seems forbidding until you consider changing variables to u = 1/x. Find a least maximum approximation for θ(x) using just two constants.