  A solution to a version of the Stieltjes moment problem is presented. Using
this solution, we construct a family of coherent states of a charged particle
in a uniform magnetic field. We prove that these states form an overcomplete
set that is normalized and solves the identity. By the help of the coherent
states we construct the Fock-Bergmann representation related to the particle
quantization. This quantization procedure takes into account a circle topology
of the classical motion.
