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The orthogonal polynomials p _n satisfy Turán’s inequality if p_n ²(x)-p_n-1(x)p_n+1(x) ≥ 0 for ≥ 1 and for all x in the interval of orthogonality. We give general criteria for orthogonal polynomials to satisfy Turán’s inequality. This yields the known results for classical orthogonal polynomials as well as new results, for example, for the q-ultraspherical polynomials.