Abstract
In the same way as the theory of series of numbers is based on the theory of sequences of numbers, the methods and results of sequences of functions set the stage for development of the theory of series of functions. This logic connection between sequences and series follows from the fact that the initial definitions and fundamental concepts of series are introduced by means of sequences: a series is usually defined as a sum of all the elements of a given sequence and the convergence (of any kind) of a series is reduced to the convergence (of the corresponding kind) of the sequence of its partial sums.
The cases of action at a distance are becoming, in a physical point of view, daily more and more important. Sound, light, electricity, magnetism, gravitation, present them as a series.Michael Faraday, 1857
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Bourchtein, L., Bourchtein, A. (2022). Series of Functions. In: Theory of Infinite Sequences and Series. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-79431-6_4
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DOI: https://doi.org/10.1007/978-3-030-79431-6_4
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Publisher Name: Birkhäuser, Cham
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