Oscillating Finite Sums

Type
Book Chapter

Authors
Alabdulmohsin, Ibrahim

KAUST Department
Computer Science Program
King Abdullah University of Science and Technology, Dhahran, Saudi Arabia

Online Publication Date
2018-03-08

Print Publication Date
2018

Date
2018-03-08

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.

Citation
Alabdulmohsin IM (2018) Oscillating Finite Sums. Summability Calculus: 93–113. Available: http://dx.doi.org/10.1007/978-3-319-74648-7_5.

Publisher
Springer Nature

Journal
Summability Calculus

DOI
10.1007/978-3-319-74648-7_5

Additional Links
https://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_5

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