Definition:Continued Fraction/Infinite

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Definition

Let $F$ be a field, such as the field of real numbers $\R$.


Informally, an infinite continued fraction in $F$ 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 $a_0, a_1, a_2, \ldots, a_n, \ldots \in F$.


Formally, an infinite continued fraction in $F$ is a sequence, called a sequence of partial denominators, whose domain is $\N_{\ge 0}$.


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, and is also known as a nonterminating (continued) fraction.


Also see


Sources