A q-generalization of the para-Racah polynomials

New bispectral orthogonal polynomials are obtained from an unconventional truncation of the Askey-Wilson polynomials. In the limit q→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.