Abstract
The transformations \(S_n(w) := a_n/(b_n + w)\) are linear fractional transformations with \(S_n(\infty) = 0\) Hence Sn := s1 ο s2 ο…ο sn are linear fractional transformations with \(S_n(\infty) = S_{n-1}(0)\) and a continued fraction is essentially a sequence of linear fractional transformations {Sn} with \(S_n(\infty) = S_{n-1}(0)\) for all n It is therefore natural to define convergence of continued fractions as convergence of {Sn} in some sense.
Keywords
- Recurrence Relation
- Continue Fraction
- Equivalence Transformation
- General Convergence
- Exceptional Sequence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Atlantis Press/World Scientific
About this chapter
Cite this chapter
Lorentzen, L., Waadeland, H. (2008). Basics. In: Continued Fractions. Atlantis Studies in Mathematics for Engineering and Science, vol 1. Atlantis Press. https://doi.org/10.2991/978-94-91216-37-4_2
Download citation
DOI: https://doi.org/10.2991/978-94-91216-37-4_2
Publisher Name: Atlantis Press
Online ISBN: 978-94-91216-37-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)