On a monotonic trigonometric sum
type: Item
instance of: scholarly article
title: On a monotonic trigonometric sum
zbMATH Open document ID: 0869.42002
DOI: 10.1007/BF01305965
author: Gavin Brown
author: Stamatis Koumandos
published in: Monatshefte für Mathematik
publication date: 1997-08-24T00:00:00Z
full work available at URL: https://eudml.org/doc/178763
review text: The main result is the Theorem: For \(n\in\mathbb{N}\), \(\theta\in(0,\pi)\) and \(\alpha\geq 1\), \[ {d\over d\theta} \Biggl(\cos{\theta\over 2} \Biggl(1+ \sum^n_{k=1} {\cos k\theta\over k^\alpha}\Biggr)\Biggr)<0. \] This inequality fails to hold for appropriate \(n\) and \(\theta\) when \(0<\alpha<1\).
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 42A32
zbMATH DE Number: 986869
zbMATH Keywords: positive trigonometric sums
zbMATH Keywords: Fourier series
reviewed by: Wang Kunyang
MaRDI profile type: Publication
cites work: A Monotonic Trigonometric Sum
cites work: Positivity of some basic cosine sums
cites work: Positive Sums of the Classical Orthogonal Polynomials
cites work: Q4861743
cites work: Q3267566
cites work: Q3254471
description: scientific article; zbMATH DE number 986869