Analytic Summability Theory

Handle URI:
http://hdl.handle.net/10754/627441
Title:
Analytic Summability Theory
Authors:
Alabdulmohsin, Ibrahim M.
Abstract:
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose prototypical examples include the Abel summation method, the Cesaro means, and the Borel summability method. As will be established in subsequent chapters, the theory of summability of divergent series is intimately connected to the theory of fractional finite sums. In this chapter, we introduce a generalized definition of series as well as a new summability method for computing the value of series according to such a definition. We show that the proposed summability method is both regular and linear, and that it arises quite naturally in the study of local polynomial approximations of analytic functions. The materials presented in this chapter will be foundational to all subsequent chapters.
KAUST Department:
King Abdullah University of Science and Technology, Dhahran, Saudi Arabia
Citation:
Alabdulmohsin IM (2018) Analytic Summability Theory. Summability Calculus: 65–91. Available: http://dx.doi.org/10.1007/978-3-319-74648-7_4.
Publisher:
Springer International Publishing
Journal:
Summability Calculus
Issue Date:
7-Mar-2018
DOI:
10.1007/978-3-319-74648-7_4
Type:
Book Chapter
Additional Links:
https://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_4
Appears in Collections:
Book Chapters

Full metadata record

DC FieldValue Language
dc.contributor.authorAlabdulmohsin, Ibrahim M.en
dc.date.accessioned2018-04-15T07:13:34Z-
dc.date.available2018-04-15T07:13:34Z-
dc.date.issued2018-03-07en
dc.identifier.citationAlabdulmohsin IM (2018) Analytic Summability Theory. Summability Calculus: 65–91. Available: http://dx.doi.org/10.1007/978-3-319-74648-7_4.en
dc.identifier.doi10.1007/978-3-319-74648-7_4en
dc.identifier.urihttp://hdl.handle.net/10754/627441-
dc.description.abstractThe theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose prototypical examples include the Abel summation method, the Cesaro means, and the Borel summability method. As will be established in subsequent chapters, the theory of summability of divergent series is intimately connected to the theory of fractional finite sums. In this chapter, we introduce a generalized definition of series as well as a new summability method for computing the value of series according to such a definition. We show that the proposed summability method is both regular and linear, and that it arises quite naturally in the study of local polynomial approximations of analytic functions. The materials presented in this chapter will be foundational to all subsequent chapters.en
dc.publisherSpringer International Publishingen
dc.relation.urlhttps://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_4en
dc.titleAnalytic Summability Theoryen
dc.typeBook Chapteren
dc.contributor.departmentKing Abdullah University of Science and Technology, Dhahran, Saudi Arabiaen
dc.identifier.journalSummability Calculusen
kaust.authorAlabdulmohsin, Ibrahim M.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.