An inequality for Tchebycheff polynomials and extensions

Richard Askey, George Gasper, Lawrence A. Harris

Research output: Contribution to journalArticlepeer-review

Abstract

The inequality Tn(xy) ≤ Tn(x) Tn(y), x, y ≥ 1, where Tn(x) is the Tchebycheff polynomial of the first kind, can be proven very easily by use of one of the extremal properties of these polynomials. It also follows from ( d2 du2) log Tn(eu) ≤ 0, u ≥ 0. Various proofs are given for these inequalities and for generalizations to other classes of polynomials.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Approximation Theory
Volume14
Issue number1
DOIs
StatePublished - May 1975

Bibliographical note

Funding Information:
* Research supported in part by NSF Grant GP-33897. + Research supported in part by NSF Grant GP-32116 and in part by the Alfred Foundation. * Research supported in part by NSF Grant GP-33117.

Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics (all)
  • Applied Mathematics

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