  We determine closed and compact expressions for the epsilon-expansion of
certain Gaussian hypergeometric functions expanded around half-integer values
by explicitly solving for their recurrence relations. This epsilon-expansion is
identified with the normalized solution of the underlying Fuchs system of four
regular singular points. We compute its regularized zeta series (giving rise to
two independent associators) whose ratio gives the epsilon-expansion at a
specific value. Furthermore, we use the well known one-loop massive bubble
integral as an example to demonstrate how to obtain all-order
epsilon-expansions for Feynman integrals and how to construct representations
for Feynman integrals in terms of generalized hypergeometric functions. We use
the method of differential equations in combination with the recently
established general solution for recurrence relations with non-commutative
coefficients.
