continued fraction

Noun

 * 1)  A compound numerical expression consisting of an integer plus a fraction whose numerator is a positive integer and whose denominator is a continued fraction (an integer plus a fraction), and so on, with finite or infinite recursion.
 * 2) * 2000, Andrew Zardecki, 18: Continued Fractions in Time Series Forec[a]sting, Da Ruan (editor), Fuzzy Systems and Soft Computing in Nuclear Engineering,, 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.
 * 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.

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. (See )

Translations

 * Finnish: ketjumurtoluku
 * French: fraction continue
 * German:
 * Icelandic: keðjubrot
 * Italian: frazione continua
 * Polish: ułamek łańcuchowy
 * Swedish: