Large-q expansion of the energy and magnetization cumulants for the two-dimensional q-state Potts model

We have calculated the large-q expansion for the energy cumulants and the magnetization cumulants at the phase transition point in the two-dimensional q-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirms us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior not only of the energy cumulants but also of the magnetization cumulants for $q \to 4_+$.