Progress with large Nf β-functions

We report on the progress in the computation of the β-functions of φ4 theory and QCD in the large N expansion. For the former we give an analytic formula for the critical exponent which encodes higher order coefficients in the series beyond those currently known in the MS scheme at O(1/N2) in a large N expansion. This allows us to deduce new coefficients in the field anomalous dimension which relate to Kreimer's knot theory of the divergences of a quantum field theory. A similar exponent is computed for the β-function of QCD at O(1/Nf). (orig.)