Computes the single particle functions z(k \beta) and their derivatives dz(k\beta)/d\beta for a
system of npart bosons in a cubic box of side L with periodic boundary conditions, and at the temperature
T = 1/(k_B \beta) measured in units of the ideal gas BEC condensation temperature Tc0.
Tc0 = 2 \pi \hbar^2 / m * (( npart/L^3 ) / \zeta(3/2))^(3/2)