Integral and discrete representations of some Hq-semiclassical forms

The aim of this paper is to deduce integral and discrete representations of some Hq-semiclassical forms of class one. These forms were studied by B. Bouras and F. Marcellan in [1], (Quadratic decomposition of a family of Hq-semiclassical orthogonal polynomial sequences, J. Difference Equ. Appl. 18 (2012), 2039{2057), but unfortunately, the above problem of representation remained opened in that work. In this paper, we find the moments investigate the of theses forms to solve this problem.Keywords: q-difference operator, Hq-semi-classical polynomials, integral representation, q-difference equations, q-series representation