  Reduced exciton mass, polarizability, and dielectric constant of the
surrounding medium are essential properties for semiconducting materials, and
they have been extracted recently from the magnetoexciton energies. However,
the acceptable accuracy of the suggested method requires very high magnetic
intensity. Therefore, in the present paper, we propose an alternative method of
extracting these material properties from recently available experimental
magnetoexciton s-state energies in monolayer transition-metal dichalcogenides
(TMDCs). The method is based on the high sensitivity of exciton energies to the
material parameters in the Rytova-Keldysh model. It allows us to vary the
considered material parameters to get the best fit of the theoretical
calculation to the experimental exciton energies for the $1s$, $2s$, and $3s$
states. This procedure gives values of the exciton reduced mass and $2D$
polarizability. Then, the experimental magnetoexciton spectra compared to the
theoretical calculation also determine the average dielectric constant.
Concrete applications are presented only for monolayers WSe$_2$ and WS$_2$ from
the recently available experimental data; however, the presented approach is
universal and can be applied to other monolayer TMDCs. The mentioned fitting
procedure requires a fast and effective method of solving the Schr\"{o}dinger
equation of an exciton in monolayer TMDCs with a magnetic field. Therefore, we
also develop such a method in this paper for highly accurate magnetoexciton
energies.
