Category:Continued Fractions
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This category contains results about Continued Fractions.
Definitions specific to this category can be found in Definitions/Continued Fractions.
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.
Subcategories
This category has the following 4 subcategories, out of 4 total.
Pages in category "Continued Fractions"
The following 24 pages are in this category, out of 24 total.
A
C
- Condition for Rational to be Convergent
- Continued Fraction Algorithm
- Continued Fraction Expansion of Irrational Number Converges to Number Itself
- Continued Fraction Expansion of Irrational Square Root
- Continued Fraction Expansion via Gauss Map
- Continued Fraction Identities/First/Infinite
- Convergents are Best Approximations
- Convergents are Best Approximations/Corollary