q-Pearson pair and moments in q-deformed ensembles

The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the q-lattice setting is considered. We take up task initiating a systematic study corresponding moments density two complementary viewpoints. first requires knowledge ensemble average with respect general Schur polynomial, which spectral follow as corollary. In case little q-Laguerre weight, particular $$_3 \phi _2$$ basic hypergeometric used express moments. second approach q-Laplace transform un-normalised measure. Using integrability properties associated q-Pearson equation for q-classical weights, fourth-order q-difference obtained, generalising result Ledoux in classical cases.