A large family of semi-classical polynomials: The perturbed Chebyshev

Some results concerning finite perturbations of order s of the Chebyshev polynomials are shown. Their semi-classical character follows from the Stieltjes transform of their orthogonality measure. According to the choice of the perturbation parameters, polynomials of arbitrary class can be generated. The second-order differential equation satisfied by these polynomials is obtained and several examples are worked out. Some particular cases of this differential equation had already been obtained by Shohat and Allaway.