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    Simple Finite Sums

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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/10754/627468
    
    Metadata
    Show full item record
    Abstract
    We will begin our treatment of summability calculus by analyzing what will be referred to, throughout this book, as simple finite sums. Even though the results of this chapter are particular cases of the more general results presented in later chapters, they are important to start with for a few reasons. First, this chapter serves as an excellent introduction to what summability calculus can markedly accomplish. Second, simple finite sums are encountered more often and, hence, they deserve special treatment. Third, the results presented in this chapter for simple finite sums will, themselves, be used as building blocks for deriving the most general results in subsequent chapters. Among others, we establish that fractional finite sums are well-defined mathematical objects and show how various identities related to the Euler constant as well as the Riemann zeta function can actually be derived in an elementary manner using fractional finite sums.
    Citation
    Alabdulmohsin IM (2018) Simple Finite Sums. Summability Calculus: 21–54. Available: http://dx.doi.org/10.1007/978-3-319-74648-7_2.
    Publisher
    Springer Nature
    Journal
    Summability Calculus
    DOI
    10.1007/978-3-319-74648-7_2
    Additional Links
    https://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_2
    ae974a485f413a2113503eed53cd6c53
    10.1007/978-3-319-74648-7_2
    Scopus Count
    Collections
    Computer Science Program; Book Chapters

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