SOME INDETERMINATE MOMENT PROBLEMS AND FREUD-LIKE WEIGHTS

We study two indeterminate Hamburger moment problems and the correspon ding orthogonal polynomials. The coefficients in their recurrence rela tions are of exponential growth or are polynomials of degree 2. The en tire functions in the Nevanlinna parametrization are found. The orthog onal polynomials with polynomial recurrence coefficients resemble the Freud polynomials with a = 1/2. Inequalities are given for the largest zero and the asymptotic behavior of the largest zero is established.