Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-19T04:50:36.059Z Has data issue: false hasContentIssue false

Some explicit continued fraction expansions

Published online by Cambridge University Press:  26 February 2010

M. Mendes France
Affiliation:
Professor Michel mendés France, UER de Mathématiques et d'Informatique, Université Bordeaux 1, 351, cours de la Libération, F-33405 Talence cedex, France.
A. J. van der Poorten
Affiliation:
Professor Michel mendés France, UER de Mathématiques et d'Informatique, Université Bordeaux 1, 351, cours de la Libération, F-33405 Talence cedex, France.
Get access

Extract

We determine infinite products in the field of Laurent series with the property that the truncations of the product yield every second continued fraction convergent of the product. We mention some related examples and specialize to obtain numerical results.

Type
Research Article
Copyright
Copyright © University College London 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

B-MF. Blanchard, André et , Michel Mendes France. Symétrie et transcendance. Bull. Sc. Math., 2e série, 106 (1982), 325335.Google Scholar
B-S. Baum, Leonard E. and Sweet., Melvin M. Continued fractions of algebraic power series in characteristic 2. Annals of Math., 103 (1976), 593610.CrossRefGoogle Scholar
C. Cobham, Alan. On the base dependence of sets of numbers recognizable by finite automata. Math. Systems Theory, 3 (1969), 186192.Google Scholar
L-vdP. Loxton, J. H. and Poorten, A. J. van der. Arithmetic properties of finite automata: regular sequences. J. für Math., 392 (1988), 5769.Google Scholar