  The long-standing problem of representing the general massive one-loop
Feynman integral as a meromorphic function of the space-time dimension $d$ has
been solved for the basis of scalar one- to four-point functions with indices
one. In 2003 the solution of difference equations in the space-time dimension
allowed to determine the necessary classes of special functions: self-energies
need ordinary logarithms and Gauss hypergeometric functions $_2F_1$, vertices
need additionally Kamp\'{e} de F\'{e}riet-Appell functions $F_1$, and box
integrals also Lauricella-Saran functions $F_S$. In this study, alternative
recursive Mellin-Barnes representations are used for the representation of
$n$-point functions in terms of $(n-1)$-point functions. The approach enabled
the first derivation of explicit solutions for the Feynman integrals at
arbitrary kinematics. In this article, we scetch our new representations for
the general massive vertex and box Feynman integrals and derive a numerical
approach for the necessary Appell functions $F_1$ and Saran functions $F_S$ at
arbitrary kinematical arguments.
