Definition:Continued Fraction Expansion

Definition
By definition, a continued fraction equals its sequence of partial quotients.

Therefore, to reduce the cumbersome nature of its representation, the continued fraction in the definitions are usually written as:


 * $\left[{a_1, a_2, a_3, \ldots, a_n}\right]$

for the finite case, and:
 * $\left[{a_1, a_2, a_3, \ldots}\right]$

for the infinite case.

Such an expression is known as the continued fraction expansion of the continued fraction, especially in the case of the infinite version.

For example:
 * $\left[{1, 2, 3}\right] = 1 + \cfrac 1 {2 + \cfrac 1 3}$