  For certain dimensionally-regulated one-, two- and three-loop diagrams,
problems of constructing the epsilon-expansion and the analytic continuation of
the results are studied. In some examples, an arbitrary term of the
epsilon-expansion can be calculated. For more complicated cases, only a few
higher terms in epsilon are obtained. Apart from the one-loop two- and
three-point diagrams, the examples include two-loop (mainly on-shell)
propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some
new relations involving Clausen function, generalized log-sine integrals and
certain Euler--Zagier sums are established, and some useful results for the
hypergeometric functions of argument 1/4 are presented.
