continued fraction

Definitions

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.

Equivalents

Examples

“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 Forec[a]sting⟳, 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.”

“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.”

CEFR level