We can solve the equation for the grand potential by integrating the Taylor series of the integrand term by term, or by realizing that it is proportional to the Mellin transform of the Li1(z exp(-β E)) where Lis(x) is the polylogarithm function.
We can solve the equation for the grand potential by integrating the Taylor series of the integrand term by term, or by realizing that it is proportional to the Mellin transform of the Li1(z exp(-β E)) where Lis(x) is the polylogarithm function.