Oscillating Finite Sums

Ibrahim Alabdulmohsin

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter, we use the theory of summability of divergent series, presented earlier in Chap. 4, to derive the analogs of the Euler-Maclaurin summation formula for oscillating sums. These formulas will, in turn, be used to perform many remarkable deeds with ease. For instance, they can be used to derive analytic expressions for summable divergent series, obtain asymptotic expressions of oscillating series, and even accelerate the convergence of series by several orders of magnitude. Moreover, we will prove the notable fact that, as far as the foundational rules of summability calculus are concerned, summable divergent series behave exactly as if they were convergent.
Original languageEnglish (US)
Title of host publicationSummability Calculus
PublisherSpringer Nature
Pages93-113
Number of pages21
ISBN (Print)9783319746470
DOIs
StatePublished - Mar 8 2018

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