Abstract
The theory of distributions has a flavor similar to the theory of summation of divergent series and integrals and, as we have seen in Chapter 6, is closely related to the theory of singular integrals. A generic alternating series
is a good example here. It seems to make no sense to assign a specific value to this infinite sum. Nevertheless, mathematicians have produced certain reasonable rules of summation that assign to it value 1/2. Such an assignment is in complete agreement with the intuition of physicists who encounter similar series. In this chapter, we will see how one can sum this, or even more strange, divergent series and integrals. To gain a better insight into the essence of this problem, let us begin with elementary examples and recall basic notions and theorems of the ordinary theory of convergent infinite series.
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© 1997 Birkhäuser Boston
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Saichev, A.I., Woyczyński, W.A. (1997). Summation of Divergent Series and Integrals. In: Distributions in the Physical and Engineering Sciences. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4158-4_8
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DOI: https://doi.org/10.1007/978-1-4612-4158-4_8
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8679-0
Online ISBN: 978-1-4612-4158-4
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