Definition:Continued Fraction/Infinite

Definition
Informally, an infinite continued fraction is an expression of the form:


 * $a_0 + \cfrac 1 {a_1 + \cfrac 1 {a_2 + \cfrac 1 {\ddots \cfrac {} {a_{n-1} + \cfrac 1 {a_n + \cfrac 1 {\ddots}}} }}}$

where $a_0 \in \R$ is any real number and $a_1, a_2, \ldots, a_n, \ldots$ is any infinite sequence in $\R_{\ne 0}$.

Formally, an infinite continued fraction in $\R$ is a real sequence, called sequence of partial quotients, whose domain is $\N_{\geq 0}$.

An infinite continued fraction should not be confused with its value, when it exists.

Also known as
An infinite continued fraction is often abbreviated ICF.

Also see

 * Definition:Value of Infinite Continued Fraction