continued fraction


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con·tin·ued fraction

(kən-tĭn′yo͞od)
n.
A whole number plus a fraction whose numerator is a whole number and whose denominator is a whole number plus a fraction that has a denominator consisting of a whole number plus a fraction, and so on, such as 2 + 1/(3 + 7/(1 + 2/3)).
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

continued fraction

n
(Mathematics) a number plus a fraction whose denominator contains a number and a fraction whose denominator contains a number and a fraction, and so on
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

contin′ued frac′tion


n.
a fraction whose denominator contains a fraction whose denominator contains a fraction and so on.
[1860–65]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.continued fraction - a fraction whose numerator is an integer and whose denominator is an integer plus a fraction whose numerator is an integer and whose denominator is an integer plus a fraction and so on
fraction - the quotient of two rational numbers
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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Any finite continued fraction represents a rational number [8].
Then, expanding (3) into a continued fraction by the Euclidean algorithm, we obtain the block diagram of the regulator shown in Fig.
This, together with the fact that well-approximations come from the continued fraction, allows us to arrive at our desired estimate.
We give 2-, 4-, 8- and 16-dissections of a continued fraction of order sixteen.
In extreme cases, it is the sum of partial fractions or a continued fraction of the analyzed dynamic characteristic [Y.sub.U](s) or [Z.sub.U](s) describing the dynamic properties.
As in the classical context of real numbers, we have a continued fraction algorithm in K(([X.sup.-1])).
This section presents the method of synthesizing the distribution of characteristics on a continued fraction making it possible to obtain the parameters and the model of a single-axis system.
We will be concerned with the simple continued fraction expansions of [square root of D] where D is an integer that is not perfect square.
The simple and pretty continued fraction expression suggests that there might be other pretty formulae involving [square root of 2].
It has also been stated in terms of a continued fraction by Read [Rea79], so that the Touchard-Riordan formula is:
The set of all paths (a formal language) is given by the infinite continued fraction
Among several methods, continued fraction is one of the techniques that is used to obtain transient solution.