  The stringy E-function for normal irreducible complex varieties with at worst
log terminal singularities was introduced by Batyrev. It is defined by data
from a log resolution. If the variety is projective and Gorenstein and the
stringy E-function is a polynomial, Batyrev also defined the stringy Hodge
numbers as a generalization of the Hodge numbers of nonsingular projective
varieties, and conjectured that they are nonnegative. We compute explicit
formulae for the contribution of an A-D-E singularity to the stringy E-function
in arbitrary dimension. With these results we can say when the stringy
E-function of a variety with such singularities is a polynomial and in that
case we prove that the stringy Hodge numbers are nonnegative.
