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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 {a1, a2, a3, ...} corresponds to the expression a1+1/(a2+1/(a3+...)).
  • 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 {a1, a2, ..., {b1, b2, ...}}, corresponding to an infinite sequence of terms, starting with the ai, and followed by cyclic repetitions of the bi.  »
  • 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.
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