Integral and discrete representations of some H_q-semiclassical forms

Abstract

The aim of this paper is to deduce integral and discrete representations of some H_q -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.

Mathematics Subject Classification (2010):

• 42C05
• 33C45

Keywords:

• q-difference operator
• H_q-semi-classical polynomials
• integral representation
• q-difference equations
• q-series representations