On the Krall-type polynomials on qq-quadratic lattices

In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, qq-basic series representation and three-term recurrence relations are obtained. In particular, the qq-Racah–Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard qq-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed.