  The sum of all ladder and rainbow diagrams in $\phi^3$ theory near 6
dimensions leads to self-consistent higher order differential equations in
coordinate space which are not particularly simple for arbitrary dimension D.
We have now succeeded in solving these equations, expressing the results in
terms of generalized hypergeometric functions; the expansion and representation
of these functions can then be used to prove the absence of renormalization
factors which are transcendental for this theory and this topology to all
orders in perturbation theory. The correct anomalous scaling dimensions of the
Green functions are also obtained in the six-dimensional limit.
