ContinuedFraction

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.

Further Examples