A General Theorem on the Conditional Convergence of Trigonometric Series

Edgar A. Cohen Jr.

doi:10.4236/ojdm.2013.31003

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A General Theorem on the Conditional Convergence of Trigonometric Series

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DOI: 10.4236/ojdm.2013.31003 4,841 Downloads 7,221 Views

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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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

E. Cohen Jr., "A General Theorem on the Conditional Convergence of Trigonometric Series," Open Journal of Discrete Mathematics, Vol. 3 No. 1, 2013, pp. 16-17. doi: 10.4236/ojdm.2013.31003.

References

[1]	D. V. Widder, “Advanced Calculus,” 2nd Edition, Prentice Hall, Inc., Englewood Cliffs, 1961, pp. 333-335.

[2]	W. Rogosinski, “Fourier Series,” 2nd Edition, Chelsea Publishing Company, New York, 1959, p. 18.

[3]	I. Niven, “Irrational Numbers,” The Mathematical Association of America, Washington DC, 1956, pp. 72-81

[4]	E. C. Titchmarsh, “The Theory of Functions,” 2nd Edition, Oxford University Press, Amen House, London, 1939, p. 420.