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Our aim is to characterize a large family of  H q  -semiclassical orthogonal  q -polynomial sequences of class one verifyingβ  n   =    (  -  1  )   n${\beta _n=(-1)^n}$   ,n  ≥  0    ${n\ge 0}$   , 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 areH   q  2${H_{q^2}}$   -classical allows us to establish the recurrence elements and integral representation and discrete measure.

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