Skip Navigation

Journal of the London Mathematical Society 2004 69(3):639-656; doi:10.1112/S0024610704005253
© 2004 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Alzer, H.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

On Ramanujan's Inequalities for exp(k)

Horst Alzer

Morsbacher Straße 10, D-51545 Waldbröl, Germany, alzerhorst{at}freenet.de

Received 1 October 2003.

Ramanujan claimed in his first letter to Hardy (16 January 1913) that


Formula

where {theta}(k) lies between 2/21 and 8/45. This conjecture was proved in 1995 by Flajolet et al. The paper establishes the following refinement.


Formula

where


Formula

Both bounds for {theta}*(k) are sharp.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.