  The Gauss hypergeometric functions 2F1 with arbitrary values of parameters
are reduced to two functions with fixed values of parameters, which differ from
the original ones by integers. It is shown that in the case of integer and/or
half-integer values of parameters there are only three types of algebraically
independent Gauss hypergeometric functions. The epsilon-expansion of functions
of one of this type (type F in our classification) demands the introduction of
new functions related to generalizations of elliptic functions. For the five
other types of functions the higher-order epsilon-expansion up to functions of
weight 4 are constructed. The result of the expansion is expressible in terms
of Nielsen polylogarithms only. The reductions and epsilon-expansion of q-loop
off-shell propagator diagrams with one massive line and q massless lines and
q-loop bubble with two-massive lines and q-1 massless lines are considered. The
code (Mathematica/FORM) is available via the www at this URL
http://theor.jinr.ru/~kalmykov/hypergeom/hyper.html
