  In this paper we calculate at high-precision the expansions in e=(4-D)/2 of
the master integrals of 4-loop vacuum bubble diagrams with equal masses, using
a method based on the solution of systems of difference equations. We also show
that the analytical expression of a related on-shell 3-loop self-mass master
integral contains new transcendental constants made up of complete elliptic
integrals of first and second kind.
