Explore the consequences of using the full version of Stirlings approximation, x!(2) 1/2 x x+1/2 e x

Explore the consequences of using the full version of Stirling’s approximation, x!≈(2π)^1/2x^x+1/2e^−x, in the development of the expression for the configuration of greatest weight. Does the more accurate approximation have a significant effect on the form of the Boltzmann distribution?