  The large-n expansion is applied to the calculation of thermal critical
exponents describing the critical behavior of spatially anisotropic
d-dimensional systems at m-axial Lifshitz points. We derive the leading
nontrivial 1/n correction for the perpendicular correlation-length exponent
nu_{L2} and hence several related thermal exponents to order O(1/n). The
results are consistent with known large-n expansions for d-dimensional critical
points and isotropic Lifshitz points, as well as with the second-order epsilon
expansion about the upper critical dimension d^*=4+m/2 for generic m\in[0,d].
Analytical results are given for the special case d=4, m=1. For uniaxial
Lifshitz points in three dimensions, 1/n coefficients are calculated
numerically. The estimates of critical exponents at d=3, m=1 and n=3 are
discussed.
