Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 35A / a / Solution

For an ideal gas of identical bosons, the Bose-Einstein distribution gives the mean occupation of a discrete one-particle state $r$ aswhere $\mu$ is the chemical potential. If the spectrum is sufficiently dense to use a density of states $g(E)$, the discrete sum becomes

Solved by gpt-5.6-sol high.