Definition:Continued Fraction/Simple

Definition
Let:
 * $a_1 + \cfrac 1 {a_2 + \cfrac 1 {a_3 + \cfrac 1 {\ddots \cfrac {} {a_{n-1} + \cfrac 1 {a_n + \cfrac 1 {\ddots}}} }}}$

be a continued fraction, either finite or infinite.

Let all the partial quotients $a_1, a_2, a_3, \ldots$ be integers.

Then the continued fraction is a simple continued fraction.

Simple Infinite Continued Fraction
When the context is such that it is immaterial whether a simple continued fraction is finite or infinite, the abbreviation SCF can be used.

Also known as
A simple continued fraction is also known as a regular continued fraction.