A General Theorem on the Conditional Convergence of Trigonometric Series

DOI: 10.4236/ojdm.2013.31003   PDF   HTML   XML   4,973 Downloads   7,422 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.

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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.

  
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