The generalization of the highly accurate exponential variational expa
nsion in the relative coordinates r(32), r(31), and r(21) is presented
for the computation of bound states with arbitrary values of the tota
l angular momentum L and space parity pi for three-body nonrelativisti
c systems with arbitrary particle masses. For all matrix elements expl
icit analytical formulas are presented which have relatively simple st
ructures and contain L and pi as parameters.