  Basing on Mellin-Barnes representations and Miller's transformation, we
present the Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of 4-loop
vacuum Feynman integrals with arbitrary masses. Through the GKZ hypergeometric
systems, the analytical hypergeometric solutions of 4-loop vacuum Feynman
integrals with arbitrary masses can be obtained in neighborhoods of origin
including infinity. The analytical expressions of 4-loop vacuum Feynman
integrals can be formulated as a linear combination of the fundamental solution
systems in certain convergent region.
