Large-$q$ expansion of the two-dimensional $q$-state Potts model by the finite lattice method

We have calculated the large-$q$ expansion for the energy and magnetization cumulants at the first order phase transition point in the two-dimensional $q$-state Potts model to the 21st or 23rd order in $1\mathrm{/}\sqrt{q}$ using the finite lattice method. The obtained series allow us to give highly convergent estimates of the cumulants for $q>4$. The results confirm us the correctness of the conjecture by Bhattacharya {\em et al.} on the asymptotic behavior of the energy cumulants for $q\to 4_{+}$ and a similar new conjecture on the magnetization cumulants.