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.
|Number of pages||11|
|Journal||Journal of Approximation Theory|
|State||Published - May 1975|
Bibliographical noteFunding 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 2014 Elsevier B.V., All rights reserved.
ASJC Scopus subject areas
- Numerical Analysis
- Mathematics (all)
- Applied Mathematics