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BUILT-IN MATHEMATICA SYMBOL
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.
Details
- The continued fraction representation
corresponds to the expression 
. - x can be either an exact or an inexact number.
- 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,
is always equivalent to 
; ContinuedFraction returns the first of these forms. - FromContinuedFraction[list] reconstructs a number from the result of ContinuedFraction.
Examplesopen all
Basic Examples (1)
20 terms in the continued fraction for 
:
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New in 4
