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 on the web: Section 3.2.4.
Implementation Notes: see section A.9.4.
See also: FromContinuedFraction, IntegerDigits, Rationalize, RealDigits.
Further Examples
