  A reduction theorem is proved for functionals of Gamma-correlated random
fields with long-range dependence in d-dimensional space. In the particular
case of a non-linear function of a chi-squared random field with Laguerre rank
equal to one, we apply the Karhunen-Lo\'eve expansion and the Fredholm
determinant formula to obtain the characteristic function of its
Rosenblatt-type limit distribution. When the Laguerre rank equals one and two,
we obtain the multiple Wiener-It\^o stochastic integral representation of the
limit distribution. In both cases, an infinite series representation in terms
of independent random variables is constructed for the limit random variables.
