where ζ (α) is the Riemann zeta function (using Li α (1) = ζ (α)). Thus, for a fixed number of particles N m, the largest possible value that β can have is a critical value β c. This corresponds to a critical temperature T c = 1/ k B β c, below which the Thomas–Fermi approximation breaks down (the continuum of states simply can no longer support this many particles, at lower temperatures). The above equation can be solved for the critical temperature: