Brown, B. M.; Evans, W. D.; Littlejohn, L. L. Discrete inequalities, orthogonal polynomials and the spectral theory of difference operators. (English) Zbl 0761.39007 Proc. R. Soc. Lond., Ser. A 437, No. 1900, 355-373 (1992). It was shown in a recent paper of the first two authors that the validity of Copson’s inequality and the value of the best constant are determined in terms of the so-called Hellinger-Nevanlinna \(m\)-function. The theory is the discrete analogue of that established by the second author and W. N. Everitt for a class of integro-differential inequalities [ibid. 380, 447-486 (1982; Zbl 0487.26005)].In this paper the properties of the \(m\)-function 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. Reviewer: A.D.Mednykh (Novosibirsk) Cited in 3 Documents MSC: 39A70 Difference operators 26D10 Inequalities involving derivatives and differential and integral operators 44A60 Moment problems Keywords:Copson’s inequality; best constant; Hellinger-Nevanlinna \(m\)-function; integro-differential inequalities; orthogonal polynomials; Hamburger moment problem; series inequalities Citations:Zbl 0487.26005 PDFBibTeX XMLCite \textit{B. M. Brown} et al., Proc. R. Soc. Lond., Ser. A 437, No. 1900, 355--373 (1992; Zbl 0761.39007) Full Text: DOI