Generating functions for K-theoretic Donaldson invariants and Le Potier's strange duality

K-theoretic Donaldson invariants are holomorphic Euler characteristics of determinant line bundles on moduli spaces of sheaves on surfaces. We compute generating functions of K-theoretic Donaldson invariants on the projective plane and rational ruled surfaces. We apply this result to prove some cases of Le Potier’s strange duality.