An Essay on Continued Fractions
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Date
1985
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Springer-Verlag : New York, N.Y.
Abstract
The paper translated here, "De Fractionibus Continuis Dissertatio", represents
Euler's first published work on the theory of continued fractions, a subject to
which he often returned during his long career. The emphasis is on basic identities
and analytic theory, culminating in the development of the continued fraction
expansion for e. A discussion of the periodic continued fractions associated with
quadratic irrationalities is also included, but applications to number theory come
in later publications. Readers interested in mathematical system theory will be concerned primarily with Euler's treatment of the Riccati equation, Sections 28-33. This aspect of the
paper sewed as the chief motivation for the translation project.
We are grateful to C. I. Bymes for suggesting that we translate this paper.
and for his continuing support. Thanks for comments and help with references
also to C. Bernlohr, P. Fuhrmann, W. Gragg, A. Lindquist, C. Martin, L. F.
Meyers. A. Weil, H. Wimmer, and especially to 1. Burckhardt and G. Mislin of
the Euler Commission. As far as the translators know, no translation into English
or another modern language has been published.
Description
English translation of the paper: "De Fractionibus Continuis Dissertatio" by Leonhard Euler.
Article previously published in the journal: Mathematical Systems Theory, Vol. 18, pages 295-328.
Article previously published in the journal: Mathematical Systems Theory, Vol. 18, pages 295-328.
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Citation
Math. Systems Theory 18, 295-328 (1985)