The present paper aims at investigating the effect of rotation up to third order in the angular velocity of a star on p and g modes , based on the formalism developed by Soufi et al .
( 1998 ) .
Our ultimate goal is the study of oscillations of \beta Cephei stars which are often rapidly rotating stars .
Our study shows that the third-order perturbation formalism presented by Soufi et al .
( 1998 ) must be corrected for some missing terms and some misprints in the equations .
As a first step in our study of \beta 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 _ { \odot } .
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 order of 0.01 \% of the frequency for radial order n = 6 and reaches up to 0.5 \% for n = 14 .