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A Positive Functional Bound for Certain Sine Sums

Authors:

Koumandos Stamatis

Institution:

(1) Department of Mathematics and Statistics, The University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus e-mail

Abstract:

The positivity of the sine sums

$\sum\limits_{k = 1}^n {\frac{{\sin k\theta }}{{k + 1}}}$

> in (0,

) has been established by G. Brown and D. C. Wilson. In this paper, we sharpen this result by giving a positive functional estimate from below for these sine sums which does not depend on n. The corresponding problem for a more general class of sine sums is also discussed.

Keywords:

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