Hermite-Lagrange interpolation and Schur's expansion of sin \(\pi\) x
type: Item
instance of: scholarly article
title: Hermite-Lagrange interpolation and Schur's expansion of sin \(\pi\) x
zbMATH Open document ID: 0659.41005
DOI: 10.1016/0021-9045(88)90072-X
author: Gerd Berger
author: Manfred Tasche
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: With the help of Taylor's formula in the theory of right-invertible operators, a new constructive approach to the Hermite-Lagrange 2-point interpolation polynomial with explicit remainder and to Schur's expansion of sin \(\pi\) x is presented. This improve earlier results of I. Schur, G. C. Rota, D. Kahaner, A. Odlyzko, S. Wrigge, and A. Fransen. Also, we prove: If \(f\in C^{\infty}(0,1)\) is completely convex, then \(f(x)=\sum^{\infty}_{n=0}\frac{1}{n!}(a_ n+b_ nx)(x(1-x))^ n,\) \(a_ n\geq 0\), \(a_ n+b_ n\geq 0\), uniformly in (0,1).
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4077925
zbMATH Keywords: Taylor's formula
zbMATH Keywords: right-invertible operators
zbMATH Keywords: Hermite-Lagrange 2-point interpolation polynomial
zbMATH Keywords: Schur's expansion
reviewed by: Yongsheng Sun
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4077925