Review

Integral and discrete representations of some H _q-semiclassical forms

Published in: Quaestiones Mathematicae
Volume 39 , issue 3 , 2016 , pages: 341–350

DOI: 10.2989/16073606.2015.1072854

Author(s): Manoubi Mejri , , , , Tunisia

Keywords: Primary: 42C05 , Secondary: 33C45 , q-difference operator , H _q-semi-classical polynomials , integral representation , q-difference equations , q-series representations

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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.

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