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:
Also see
Special cases
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continued fraction
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continued fraction