Normalized Hough functions computed as functions of the colatitude (θ) for 0 ≤ n ≤ 5 (gravity modes) and various values of ν = (2Ω) /σ. Top-left: ν = 0; top-right: ν = 0.8; middle-left: ν = 1.2; middle-right: ν = 2; bottom-left: ν = 4; bottom-right: ν = 12. The case ν = 0 corresponds to the normalized associated Legendre polynomials . The two plots at the top represent the regime of super-inertial waves (|ν| ≤ 1) where Hough functions look like Legendre polynomials. In the regime of sub-inertial waves (|ν| > 1), functions become more and more evanescent when |ν| increases, and oscillations are trapped around the equator in the interval [θ_ν,π−θ_ν], where .