# Category:Definitions/Continued Fractions

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This category contains definitions related to Continued Fractions.

Related results can be found in Category:Continued Fractions.

Let $n \geq 0$ 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 quotients**, whose domain is the integer interval $\left[0 \,.\,.\, n\right]$.

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

## Pages in category "Definitions/Continued Fractions"

The following 60 pages are in this category, out of 60 total.

### C

- Definition:Complete Quotient
- Definition:Continued Fraction
- Continued Fraction Algorithm/Proof 1
- Definition:Continued Fraction Expansion
- Definition:Continued Fraction Expansion of Irrational Number
- Definition:Continued Fraction Expansion of Laurent Series
- Definition:Continued Fraction Expansion of Rational Number
- Definition:Continued Fraction Expansion of Real Number
- Definition:Continued Fraction in Canonical Form
- Definition:Continued Fraction of Irrational Number
- Definition:Continued Fraction of Real Number
- Definition:Continued Fraction/Expansion of Real Number
- Definition:Continued Fraction/Finite
- Definition:Continued Fraction/Infinite
- Definition:Continued Fraction/Notation
- Definition:Continued Fraction/Simple
- Definition:Continued Fraction/Simple/Finite
- Definition:Continued Fraction/Simple/Infinite
- Definition:Convergent Continued Fraction
- Definition:Convergent of Continued Fraction
- Definition:Convergent of Continued Fraction/Definition 1
- Definition:Convergent of Continued Fraction/Definition 2
- Definition:Convergent of Continued Fraction/Even
- Definition:Convergent of Continued Fraction/Odd
- Definition:Cycle Length of Periodic Continued Fraction
- Definition:Cycle of Periodic Continued Fraction