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Problem 73-21, A Sine Inequality

✍ Scribed by R. A. Askey

Book ID: 124934756
Publisher: Society for Industrial and Applied Mathematics
Year: 1973
Tongue: English
Weight: 162 KB
Volume: 15
Category: Article
ISSN: 0036-1445
DOI: 10.2307/2028732

No coin nor oath required. For personal study only.

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A refinement of Vietoris' inequality for

A refinement of Vietoris' inequality for sine polynomials

✍ Horst Alzer; Stamatis Koumandos; Martin Lamprecht 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 90 KB

## Abstract Let equation image where equation image In 1958, Vietoris proved that __σ~n~__ (__x__) is positive for all __n__ ≥ 1 and __x__ ∈ (0, __π__). We establish the following refinement. The inequalities equation image hold for all natural numbers __n__ and real numbers __n__ ≥ 1 and __x