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 on the web: see Section A.9.4.
See also: FromContinuedFraction, IntegerDigits, RealDigits.
Further Examples
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