a)ω_R/ω_k and b) ω_I/ω_k versus ν_ni/ω_k for the transverse kink (m = 1) mode with k_zR = 0.1, ρ_i,0/ρ_i,ex = 3, c_ie,0/c_A,0 = 0.2, and χ = 4. The solid line is the result obtained by numerically solving the dispersion relation in the absence of neutral pressure (Eq. (37)). The symbols are the approximate analytic results in the weak damping approximation (Eqs. (43) and (44)).