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dc.contributor.authorAlabdulmohsin, Ibrahim M.
dc.date.accessioned2018-04-15T07:13:34Z
dc.date.available2018-04-15T07:13:34Z
dc.date.issued2018-03-07
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.
dc.identifier.doi10.1007/978-3-319-74648-7_4
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.
dc.publisherSpringer Nature
dc.relation.urlhttps://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_4
dc.titleAnalytic Summability Theory
dc.typeBook Chapter
dc.contributor.departmentKing Abdullah University of Science and Technology, Dhahran, Saudi Arabia
dc.identifier.journalSummability Calculus
kaust.personAlabdulmohsin, Ibrahim M.


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