  We generalize techniques of Addison to a vastly larger context. We obtain
integral representations in terms of the first periodic Bernoulli polynomial
for a number of important special functions including the Lerch zeta,
polylogarithm, Dirichlet $L$- and Clausen functions. These results then enable
a variety of Addison-type series representations of functions. Moreover, we
obtain integral and Addison-type series for a variety of mathematical
constants.
