ContinuedFraction[x, n] generates a list of the first n terms in the continued fraction representation of x.
ContinuedFraction[x] generates a list of all terms that can be obtained given the precision of x.
The continued fraction representation , , , ... corresponds to the expression .
x can be either an exact or an inexact number.
Example: ContinuedFraction[Pi, 4] .
For exact numbers, ContinuedFraction[x] can be used if x is rational, or is a quadratic irrational.
For quadratic irrationals, ContinuedFraction[x] returns a result of the form , , ... , , , ... , corresponding to an infinite sequence of terms, starting with the , and followed by cyclic repetitions of the .
Since the continued fraction representation for a rational number has only a limited number of terms, ContinuedFraction[x, n] may yield a list with less than n elements in this case.
For terminating continued fractions, ... , k is always equivalent to ... , k-1, 1; ContinuedFraction returns the first of these forms.
FromContinuedFraction[list] reconstructs a number from the result of ContinuedFraction.
See The Mathematica Book: Section 3.2.4.
Implementation Notes: see section A.9.4.
See also: FromContinuedFraction, IntegerDigits, Rationalize, Khinchin, RealDigits.