Definition:Continued Fraction

Notation
A continued fraction can be denoted using ellipsis:
 * $a_0 + \cfrac 1 {a_1 + \cfrac 1 {a_2 + \cfrac 1 {\ddots \cfrac {} {}}}}$

which suggests the definition of its value, but it should be noted that this is only a notation.

By definition, a continued fraction is its sequence of partial quotients and can thus be denoted:
 * $(a_n)_{n\geq 0}$
 * $[a_0; a_1, a_2, \ldots ]$
 * $[a_0, a_1, a_2, \ldots ]$

where the last two notations are usually reserved for its value.

Also known as
A continued fraction is also known as a:
 * continued fraction in canonical form
 * regular continued fraction
 * simple continued fraction

as opposed to a generalized continued fraction.

Also see

 * Definition:Value of Continued Fraction
 * Definition:Sequence of Partial Quotients
 * Definition:Sequence of Complete Quotients
 * Definition:Convergent of Continued Fraction
 * Definition:Numerator of Continued Fraction
 * Definition:Denominator of Continued Fraction

Other continued fraction expansions

 * Definition:Continued Fraction Expansion of Real Number
 * Definition:Continued Fraction Expansion of Laurent Series
 * Definition:p-Adic Ruban Continued Fraction

Generalizations

 * Definition:Generalized Continued Fraction