  In this paper, we study the generalized Dedekind-Rademacher sums considered
by Hall, Wilson and Zagier. We establish a formula for the products of two
Bernoulli functions. The proof relies on Parseval's formula, Hurwitz's formula,
and Lerch's functional equation. The result leads to reciprocity formulas for
some generalizations of the classical Dedekind sums. In particular, it is shown
that Carlitz's, Berndt's, Hall and Wilson's reciprocity theorems are deduced as
special cases.
