Dynamics of generalizations of the AGM continued fraction of Ramanujan. Part I: divergence.
| Author(s) | Borwein, J. M. | |
| Author(s) | Luke, D. Russell | |
| Date Accessioned | 2004-12-22T02:43:12Z | |
| Date Available | 2004-12-22T02:43:12Z | |
| Publication Date | 2004-11-19 | |
| Abstract | We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were determined for certain complex parameters [4, 3, 2]. A study of the AGM continued fraction is equivalent to an analysis of the convergence of certain difference equations and the stability of dynamical systems. Using the matrix analytical tools developed in [2], we determine the convergence properties of deterministic difference equations and so divergence of their corresponding continued fractions. | en |
| Extent | 1069805 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/210 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | Technical Report: 2004-09 | |
| Keywords | Continued fractions | en |
| Keywords | Ramanujan AGM relation | en |
| Keywords | difference equations | en |
| Keywords | matrix analysis | en |
| dc.subject.classification | AMS: 11J70, 40A15 | |
| Title | Dynamics of generalizations of the AGM continued fraction of Ramanujan. Part I: divergence. | en |
| Type | Technical Report | en |