The paper discusses four analytical methods for the summation of infinite series in closed form. Many illustrative examples are given including some with direct relevance to electrical engineering subjects like Fourier analysis of circuits, potential solutions of Laplace's equation, and finite differences.
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References
1.
PipesL. A., ‘The summation of Fourier series by operation method’, J. Appl. Phys., 21, pp. 298–301, (April 1950).
2.
MacfarlaneG. G., ‘The application of Mellin transforms to the summation of slowly convergent series’, Phil. Mag., 40, pp. 188–197, (February 1949).
3.
WheelonA. D., ‘On the summation of infinite series in closed form’, J. App. Phys., 25, No. 1, pp. 113–18, (January 1954).
4.
BromwichT. J., An introduction to the theory of infinite seriesLondon, 2nd Ed., (1962).
5.
KnoppK., Theory and application of infinite series, Blackie and Son Ltd., London, 2nd Ed., (1951).
6.
ToralballaL. V., Theory of functions, Charles E. Merril Books, Ohio, U.S.A., p. 474, (1963).
7.
CollinR. E., Field Theory of guided waves, McGraw-Hill Book Company, Inc., New York, p. 583, (1960).
8.
SpiegelM. R., Laplace transforms, Schaum's Outline Series, McGraw-Hill Book Company, Inc., p. 214, (1965).
9.
WhittakerE. T.WatsonG. N., A course of numerical analysis, Oxford University Press, 4th Ed., p. 78, (1965).
10.
WylieC. R.Jr., Advanced engineering mathematics, McGraw-Hill Book Company, Inc., New York, 3rd Ed., p. 123, (1966).