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.

DetailsDetails

  • 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.
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