  The Clebsh-Gordan coefficients for the Lie algebra
  $\mathfrak{gl}_3$ in the Gelfand-Tsetlin base are calculated. In contrast to
previous papers the result is given as an explicit formula. To obtain the
result a realization of a representation in the space of functions on the group
$GL_3$ is used. The keystone fact that allows to carry the calculation of
Clebsh-Gordan coefficients is the theorem that says that functions
corresponding to Gelfand-Tsetlin base vectors can be expressed through
generalized hypergeometric functions.
