Definition:Continued Fraction

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

Also defined as
When one is primarily concerned with simple continued fractions of real numbers, it is common to require a continued fraction to have strictly positive partial quotients, except perhaps the first.

Also known as
A continued fraction is also known as a:
 * continued fraction in canonical form
 * regular continued fraction
 * simple continued fraction

as opposed to a generalized continued fraction.

Also see

 * Definition:Value of Continued Fraction
 * Definition:Sequence of Partial Quotients
 * Definition:Sequence of Complete Quotients
 * Definition:Convergent of Continued Fraction
 * Definition:Numerators and Denominators of Continued Fraction

Other continued fraction expansions

 * Definition:Continued Fraction Expansion of Real Number
 * Definition:Continued Fraction Expansion of Laurent Series
 * Definition:p-Adic Ruban Continued Fraction

Generalizations

 * Definition:Generalized Continued Fraction