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Positivity of some basic cosine sums

Published online by Cambridge University Press:  24 October 2008

Gavin Brown ,
Kun-Yang Wang  and
David C. Wilson
Gavin Brown
Affiliation:
University of Adelaide, GPO Box 498, Adelaide SA 5001, Australia
Kun-Yang Wang
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, People's Republic of China
David C. Wilson
Affiliation:
School of Mathematics, University of New South Wales, PO Box 1, Kensington NSW 2033, Australia
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Abstract

We show that all partial sums of 1 + σk−α cos kθ are non-negative for α > α0, where 0·308443 < α0 < 0·308444 and α0 is the unique root of the equation

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 3 , November 1993 , pp. 383 - 391
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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