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This is the second part of our study of the solutions of aq -discrete second Painlevé equation (q -PII ) of type (A 2 +A 1 )(1) via its iso-monodromy deformation problem. In part I, we showed how to use theq -discrete linear problem associated withq -PII to find an infinite sequence of exact rational solutions. In this paper, we study the case giving rise to an infinite sequence ofq -hypergeometric-type solutions. We find a new determinantal representation of all such solutions and solve the iso-monodromy deformation problem in closed form.

Exact solutions of a q -discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions