Simple Finite Sums

Ibrahim M. Alabdulmohsin
Additional contact information
Ibrahim M. Alabdulmohsin: King Abdullah University of Science and Technology

Chapter Chapter 2 in Summability Calculus, 2018, pp 21-54 from Springer

Abstract: 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.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-74648-7_2

Ordering information: This item can be ordered from
http://www.springer.com/9783319746487

DOI: 10.1007/978-3-319-74648-7_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().