  The review of the following results of the Refs. \cite{Sem} - \cite{Ans} is
presented: For mixed state light of $N$-mode electromagnetic field described by
Wigner function which has generic Gaussian form the photon distribution
function is obtained and expressed expliciltly in terms of Hermite polynomials
of $2N$-variables.The momenta of this distribution are calculated and expressed
as functions of matrix invariants of the dispersion matrix.The role of new
uncertainty relation depending on photon state mixing parameter is
elucidated.New sum rules for Hermite polynomials of several variables are
found.The photon statistics of polymode even and odd coherent light and
squeezed polymode Schr\"odinger cat light is qiven explicitly.Photon
distribution for polymode squeezed number states expressed in terms of
multivariable Hermite polynomials is discussed.
