  In this paper, a transformation formula under modular substitutions is
derived for a large class of generalized Eisenstein series. Appearing in the
transformation formulae are generalizations of Dedekind sums involving the
periodic Bernoulli function. Reciprocity theorems are proved for these Dedekind
sums. Furthermore, as an application of the transformation formulae, relations
between various infinite series and evaluations of several infinite series are
deduced. Finally, we consider these sums for some special cases.
