Turán inequalities for three-term recurrences with monotonic coefficients (Q719364)

The paper establishes some generalizations of the Turán inequalities for orthogonal polynomials defined by a three-term recurrence relation with monotonic coefficients. It also provides some examples with the Stieltjes-Wigert, Al-Salam-Carlitz and Meixner-Pollaczek polynomials. Furthermore, as an application, asymptotic bounds are deduced on the extreme zero of the orthogonal polynomials with polynomially growing coefficients of the three-term recurrence relation.