A General Theorem on the Conditional Convergence of Trigonometric Series

Edgar A. Cohen Jr.

doi:10.4236/ojdm.2013.31003

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Open Journal of Discrete Mathematics > Vol.3 No.1, January 2013

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

Edgar A. Cohen Jr.^*

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

DOI: 10.4236/ojdm.2013.31003 PDF HTML XML 5,141 Downloads 7,507 Views

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:

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.