Infinite Series Identities, Transformations, and Evaluations

Bruce C. Berndt
Additional contact information
Bruce C. Berndt: University of Illinois, Department of Mathematics

Chapter Chapter 9 in Ramanujan’s Notebooks, 1985, pp 232-294 from Springer

Abstract: Abstract Chapter 9 fully illustrates Hardy’s declaration in Ramanujan’s Collected Papers [15, p. xxxv], “It was his insight into algebraical formulae, transformations of infinite series, and so forth, that was most amazing.” This chapter has 35 sections containing 139 formulas of which many are, indeed, very beautiful and elegant. Ramanujan gives several transformations of power series leading to many striking series relations and attractive series evaluations. Most of Ramanujan’s initial efforts in this direction pertain to the dilogarithm and related functions. As is to be expected, these results are not new and can be traced back to Euler, Landen, Abel, and others. However, most of Ramanujan’s remaining findings on transformations of power series appear to be new.

Keywords: Positive Integer; Analytic Continuation; Evaluation Entry; Maclaurin Series; Penultimate Equality (search for similar items in EconPapers)
Date: 1985
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:978-1-4612-1088-7_10

Ordering information: This item can be ordered from
http://www.springer.com/9781461210887

DOI: 10.1007/978-1-4612-1088-7_10

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 ().