A General Theorem on the Conditional Convergence of Trigonometric Series - Open Journal of Discrete Mathematics

OJDM > Vol.3 No.1, January 2013

Open Journal of Discrete Mathematics

Volume 3, Issue 1 (January 2013)

ISSN Print: 2161-7635 ISSN Online: 2161-7643

Google-based Impact Factor: 0.39 Citations

A General Theorem on the Conditional Convergence of Trigonometric Series ()

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DOI: 10.4236/ojdm.2013.31003 5,781 Downloads 8,553 Views

Author(s)

Edgar A. Cohen Jr.^*

Affiliation(s)

Formerly of the Information Sciences Branch, Naval Surface Warfare Center, White Oak, USA.

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.

KEYWORDS

Conditionally Convergent; Steadily Decreasing Sequence; Euler’s Formula

Share and Cite:

Cohen Jr., E. (2013) A General Theorem on the Conditional Convergence of Trigonometric Series. Open Journal of Discrete Mathematics, 3, 16-17. doi: 10.4236/ojdm.2013.31003.

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