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A General Theorem on the Conditional Convergence of Trigonometric Series
Formerly of the Information Sciences Branch, Naval Surface Warfare Center, White Oak, USA
- 1 Formerly of the Information Sciences Branch, Naval Surface Warfare Center, White Oak, USA
Open Journal of Discrete Mathematics·Volume 03 (2013)·Pages 16–17·Published 29 January 2013·DOI10.4236/ojdm.2013.31003
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Abstract
The purpose of this paper is to establish, paralleling a well-known result for definite integrals, the conditional convergence of a family of trigonometric sine series. The fundamental idea is to group appropriately the terms of the series in order to show absolute divergence of the series, given the well-established result that the series as it stands is convergent.
KeywordsConditionally ConvergentSteadily Decreasing SequenceEuler’s Formula
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