Characterizations of a special family of H-q-semiclassical orthogonal q-polynomials of class one

Our aim is to characterize a large family of H-q-semiclassical orthogonal q-polynomial sequences of class one verifying beta(n) = (-1)(n), n >= 0, in the three-term recurrence relation where H-q is the Hahn's operator. Four canonical situations are obtained and the study of their corresponding quadratic components which are H-q2-classical allows us to establish the recurrence elements and integral representation and discrete measure.