  When calculating higher terms of the epsilon-expansion of massive Feynman
diagrams, one needs to evaluate particular cases of multiple inverse binomial
sums. These sums are related to the derivatives of certain hypergeometric
functions with respect to their parameters. Exploring this connection and using
it together with an approach based on generating functions, we analytically
calculate a number of such infinite sums, for an arbitrary value of the
argument which corresponds to an arbitrary value of the off-shell external
momentum. In such a way, we find a number of new results for physically
important Feynman diagrams. Considered examples include two-loop two- and
three-point diagrams, as well as three-loop vacuum diagrams with two different
masses. The results are presented in terms of generalized polylogarithmic
functions. As a physical example, higher-order terms of the epsilon-expansion
of the polarization function of the neutral gauge bosons are constructed.
