[en] The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz points is considered for general values of m in the large-n limit. It is proven that the recently obtained large-n expansions (Shpot et al 2005 J. Phys.: Condens. Matter 17 S1947) of the correlation exponents η_L2, η_L4 and the related anisotropy exponent θ are fully consistent with the dimensionality expansions to second order in ε = 4 + m/2 - d (Diehl and Shpot 2000 Phys. Rev. B 62 12338; Shpot and Diehl 2001 Nucl. Phys. B 612 340) inasmuch as both expansions yield the same contributions of order ε²/n