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    Analytic Summability Theory

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    Type
    Book Chapter
    Authors
    Alabdulmohsin, Ibrahim cc
    KAUST Department
    Computer Science Program
    King Abdullah University of Science and Technology, Dhahran, Saudi Arabia
    Date
    2018-03-08
    Online Publication Date
    2018-03-08
    Print Publication Date
    2018
    Permanent link to this record
    http://hdl.handle.net/10754/627441
    
    Metadata
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    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.
    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 Nature
    Journal
    Summability Calculus
    DOI
    10.1007/978-3-319-74648-7_4
    Additional Links
    https://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_4
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-74648-7_4
    Scopus Count
    Collections
    Computer Science Program; Book Chapters

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