Title: A $q$-generalization of the para-Racah polynomials,
Abstract: New bispectral orthogonal polynomials are obtained from an unconventional
truncation of the Askey-Wilson polynomials. In the limit $q \to 1$, they reduce
to the para-Racah polynomials which are orthogonal with respect to a quadratic
bi-lattice. The three term recurrence relation and q-difference equation are
obtained through limits of those of the Askey-Wilson polynomials. An explicit
expression in terms of hypergeometric series and the orthogonality relation are
provided. A $q$-generalization of the para-Krawtchouk polynomials is obtained
as a special case. Connections with the $q$-Racah and dual-Hahn polynomials are
also presented.