Definition:Continued Fraction/Finite

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Definition

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

Let $n \ge 0$ be a natural number.


Informally, a finite continued fraction of length $n$ in $F$ is an expression of the form:

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

where $a_0, a_1, a_2, \ldots, a_n \in F$.


Formally, a finite continued fraction of length $n$ in $F$ is a finite sequence, called sequence of partial denominators, whose domain is the integer interval $\closedint 0 n$.


A finite continued fraction should not be confused with its value, when it exists.


Also known as

A finite continued fraction can be abbreviated FCF, and is also known as:

a terminated (continued) fraction
a terminating (continued) fraction.


Also see


Special cases


Sources