  The one-loop dynamical polarization function of graphene in an external
magnetic field is calculated as a function of wavevector and frequency at
finite chemical potential, temperature, band gap, and width of Landau levels.
The exact analytic result is given in terms of digamma functions and
generalized Laguerre polynomials, and has the form of double sum over Landau
levels. Various limits (static, clean, etc) are discussed. The Thomas-Fermi
inverse length $q_F$ of screening of the Coulomb potential is found to be an
oscillating function of a magnetic field and a chemical potential. At zero
temperature and scattering rate, it vanishes when the Fermi level lies between
the Landau levels.
