Type
Book ChapterAuthors
Alabdulmohsin, Ibrahim
KAUST Department
Computer Science ProgramKing Abdullah University of Science and Technology, Dhahran, Saudi Arabia
Date
2018-03-08Online Publication Date
2018-03-08Print Publication Date
2018Permanent link to this record
http://hdl.handle.net/10754/627441
Metadata
Show full item recordAbstract
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.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 NatureJournal
Summability CalculusAdditional Links
https://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_4ae974a485f413a2113503eed53cd6c53
10.1007/978-3-319-74648-7_4