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 see

 * Definition:Value of Continued Fraction