Division of Mathematics, La Trobe University, P.O. Box 199, Bendigo 3552, Victoria, Australia
Copyright © 1999 Simon J. Smith. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
For a fixed integer and , let denote the th fundamental polynomial for Hermite–Fejér interpolation on the Chebyshev nodes . (So is the unique polynomial of degree at most which satisfies , and whose first derivatives vanish at each .) In this paper it is established that
It is also shown that is an increasing function of , and the best possible bound so that for all , and is obtained. The results generalise those for Lagrange interpolation, obtained by P. Erdős and G. Grünwald in 1938.