Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/74499
Title: On Fejér's inequalities for the Legendre polynomials
Authors: Alzer, H
Kwong, MK 
Keywords: 26D07
33C45
42C05
Inequalities
Legendre polynomials
Issue Date: 2017
Publisher: Wiley-VCH
Source: Mathematische nachrichten, 2017, p. 2 How to cite?
Journal: Mathematische nachrichten 
Abstract: We present various inequalities for the sum Sn(t)=∑k=0nPk(t),where Pk denotes the Legendre polynomial of degree k. Among others we prove that the inequalities 25(1+t)≤Sn(t)and3-12(1-t2)≤Sn(t)hold for all n≥1 and t∈[-1,1]. The constant factors 2/5 and (3-1)/2 are sharp. This refines a classical result of Fejér, who proved in 1908 that Sn(t) is nonnegative for all n≥1 and t∈[-1,1].
URI: http://hdl.handle.net/10397/74499
ISSN: 0025-584X
EISSN: 0025-584X
DOI: 10.1002/mana.201600461
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