ORTHOGONAL POLYNOMIALS AND EXTENSIONS OF COPSON INEQUALITY

This is a survey of recent results on a class of series inequalities involving second-order difference operators, which includes a well-known inequality of Copson's. A connection has been established between these inequalities and the properties of the Hellinger-Nevanlinna m-function for an associated recurrence relation Mx(n) = lambdaw(n)x(n), lambda is-an-element-of C: the validity of the inequality, the value of the best constant and the nontrivial equalising sequences (if they exist) are determined in terms of m. The function m is shown to have an integral representation in terms of a measure with respect to which polynomial solutions of the recurrence relation are orthogonal and this is used to examine a number of examples of the inequality. The best constants in some cases have only been evaluated numerically.