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/10754/627468
Metadata
Show full item recordAbstract
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 NatureJournal
Summability CalculusAdditional Links
https://link.springer.com/chapter/10.1007%2F978-3-319-74648-7_2ae974a485f413a2113503eed53cd6c53
10.1007/978-3-319-74648-7_2