Statistical Mechanics · Problem 3.3

The Grand Canonical Ensemble — R. K. Pathria

Physics — Statistical Mechanics · saddle-point-integration-stirling

Problem

Using the fact that

(1/n!)

is the coefficient of

x^n

in the power expansion of the function

\exp(x)

, derive an asymptotic formula for this coefficient by the method of saddle-point integration. Compare your result with the Stirling formula for

(n!)