We use the recent findings of Cohl [arXiv:1105.2735] and evaluate the principal and the residual values of the integral 1 −1 dt (1 − t 2) λ−1/2 (x − t) −κ−1/2 C λ n (t), with Re λ > − 1 2 , κ ∈ C, −1 < x < 1, where C λ n (t) is the Gegenbauer polynomial. For Re κ < 1 2 , we also evaluate the integrals x −1 dt (1 − t 2) λ−1/2 (x − t) −κ−1/2 C λ n (t) and 1 x… (More)