  We present exact and explicit form of the kernels $hat{K}(x, y)$ appearing in
the theory of energy correlations in the ensembles of Hermitian random matrices
with Gaussian probability distribution, see E. Brezin and S. Hikami, Phys. Rev.
E 57, 4140 and E 58, 7176 (1998). In obtaining this result we have exploited
the analogy with the method of producing exact forms of two-sided, symmetric
Levy stable laws, presented by us recently. This result is valid for arbitrary
values of parameters in question. We furnish analytical and graphical
representations of physical quantities calculated from $hat{K}(x, y)$'s.
