Abstract We aim at investigating the effect of rotation up to the third order in the angular velocity of a star on the p and g modes, based on the formalism developed by Soufi et al. Our ultimate goal is the study of oscillations of β Cephei stars which are often rapidly rotating stars. Our results show that the third-order perturbation formalism presented by Soufi et al. should be corrected for some missing terms and some misprints in the equations. As a first step in our study of β Cephei stars, we quantify by numerical calculations the effect of rotation on the oscillation frequencies of a uniformly rotating zero-age main-sequence star with 12 M⊙. For an equatorial velocity of 100 km s−1, it is found that the second- and third-order corrections for (l,m) = (2,2), for instance, are of the order of 0.01% of the frequency for radial order n = 6 and reaches up to 0.5% for n = 14.
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