Skip Navigation

Journal of the London Mathematical Society 1995 52(2):356-374; doi:10.1112/jlms/52.2.356
© 1995 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 Shackell, J.
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

Extensions of Asymptotic Fields Via Meromorphic Functions

John Shackell

University of Kent at Canterbury Canterbury, Kent CT2 7NF

Received 29 April 1992. Revision received 21 March 1994.

An asymptotic field is a special type of Hardy field in which, modulo an oracle for constants, one can determine asymptotic behaviour of elements. In a previous paper, it was shown in particular that limits of real Liouvillian functions can thereby be computed. Let F denote an asymptotic field and let f isin F. We prove here that if G is meromorphic at the limit of f (which may be infinite) and satisfies an algebraic differential equation over R(x), then F (G o f) is an asymptotic field. Hence it is possible (modulo an oracle for constants) to compute asymptotic forms for elements of F(G o f). An example is given to show that the result may fail if G has an essential singularity at lim f.


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.