  The Generalized Slater-Jastrow trial functional is a modification of the
Slater-Jastrow functional where, effectively, the argument of the Jastrow
factor can be momentum dependent. The associated Euler equations, which provide
an alternative to the usual approach via perturbation theory, are solved to
yield the firs three terms of the electron correlation energies for the two and
three dimensional electron gas at high density. In two dimensions we find
-0.4039 -0.50 r log r plus an estimated -0.87 r Ry. For three dimensions we
find 0.0622 log r -0.082 + 0.059 r log r plus an estimated -0.015 r Ry, where r
is the applicable Seitz radius in each case.
