Discrete Inequalities, Orthogonal Polynomials and the Spectral Theory of Difference Operators
Abstract
In a recent paper the first two authors studied a class of series inequalities associated with a threeterm recurrence relation which includes a wellknown inequality of Copson's. It was shown that the validity of the inequality and the value of the best constant are determined in terms of the socalled HellingerNevanlinna mfunction. The theory is the discrete analogue of that established by Everitt for a class of integrodifferential inequalities. In this paper the properties of the mfunction are investigated and connections with the theory of orthogonal polynomials and the Hamburger moment problem are explored. The results are applied to give examples of the series inequalities associated with the classical orthogonal polynomials.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 May 1992
 DOI:
 10.1098/rspa.1992.0066
 Bibcode:
 1992RSPSA.437..355B