TITLE:
A General Theorem on the Conditional Convergence of Trigonometric Series
AUTHORS:
Edgar A. Cohen Jr.
KEYWORDS:
Conditionally Convergent; Steadily Decreasing Sequence; Euler’s Formula
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.3 No.1,
January
29,
2013
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.