The Language of Finite Differences

Ibrahim M. Alabdulmohsin
Additional contact information
Ibrahim M. Alabdulmohsin: King Abdullah University of Science and Technology

Chapter Chapter 7 in Summability Calculus, 2018, pp 133-149 from Springer

Abstract: Abstract Throughout the previous chapters, we derived results using infinitesimal calculus, such as the Euler-Maclaurin summation formula, the Boole summation formula, and the methods of summability of divergent series. In this chapter, we derive analogous results using the language of finite differences, as opposed to infinitesimal derivatives. Using finite differences and the theory of summability of divergent series, we present a simple pictorial proof to the Shannon-Nyquist sampling theorem. Finally, we derive many identities that relate to the Euler constant, the Riemann zeta function, the Gregory coefficients, and the Cauchy coefficients, among others.

Keywords: Euler-Maclaurin Summation Formula; Infinitesimal Derivatives; Nyquist-Shannon Sampling Theorem; Riemann Zeta Function; Summability Calculus (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-74648-7_7

Ordering information: This item can be ordered from
http://www.springer.com/9783319746487

DOI: 10.1007/978-3-319-74648-7_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().