Hello, you have come here looking for the meaning of the word continued fraction. In DICTIOUS you will not only get to know all the dictionary meanings for the word continued fraction, but we will also tell you about its etymology, its characteristics and you will know how to say continued fraction in singular and plural. Everything you need to know about the word continued fraction you have here. The definition of the word continued fraction will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofcontinued fraction, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.
1992, G. E. Andrews, B. C. Berndt, L. Jacobsen, R. L. Lamphere, “The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks”, in Memoirs of the American Mathematical Society, volume 99, number 477, page 1:
Several results focus on the famous Rogers–Ramanujan continued fraction [47], [48, pp. 214-215], the only continued fraction appearing in Ramanujan's published papers.
2000, Andrew Zardecki, 18: Continued Fractions in Time Series Forecsting, Da Ruan (editor), Fuzzy Systems and Soft Computing in Nuclear Engineering, Physica-Verlag, Studies in Fuzziness and Soft Computing, page 397,
We achieve this by using well-known examples from the number theory pertaining to the continued fractions. Any sequence of natural numbers drawn from the probability distribution of the quotients of the continued fraction corresponding to an irrational number represents a typical sequence, in the sense that almost all sequences of quotients have this distribution.
2009, M. Welleda Baldoni, Ciro Ciliberto, G.M. Piacentini Cattaneo, translated by Daniele Gewurz, Elementary Number Theory, Cryptography and Codes, page 48:
We have seen that all rational numbers, and no other number, can be expressed as finite simple continued fractions. The main reason of interest of continued fractions, however, is in their application to the representation of irrational numbers. To that end we shall need infinite simple continued fractions.
Usage notes
The initial integer may be zero or even negative; subsequent non-numerator terms should be positive (while not strictly necessary, it is easier to prove convergence with positive terms).
Generally, it is assumed that every numerator is 1; if distinction is necessary, such a fraction may be called regular or simple or be said to be in canonical form. (See continued fraction on Wikipedia.Wikipedia )
continued fraction on Wikipedia.Wikipedia )