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A refinement of Vietoris' inequality for sine polynomials

โœ Scribed by Horst Alzer; Stamatis Koumandos; Martin Lamprecht

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
90 KB
Volume
283
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Abstract

Let

equation image

where

equation image

In 1958, Vietoris proved that ฯƒ~n~ (x) is positive for all n โ‰ฅ 1 and x โˆˆ (0, ฯ€). We establish the following refinement. The inequalities

equation image

hold for all natural numbers n and real numbers n โ‰ฅ 1 and x โˆˆ (0, ฯ€) if and only if

equation image

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