# Definition:Generalized Continued Fraction

## Definition

Let $k$ be a field.

Informally, a generalized continued fraction in $k$ is an expression of the form:

$b_0 + \cfrac {a_1} {b_1 + \cfrac {a_2} {b_2 + \cfrac {a_3} {\ddots \cfrac {} {b_{n-1} + \cfrac {a_n} {b_n + \cfrac {a_{n+1}} {\ddots}}} }}}$

Formally, a generalized continued fraction in $k$ is a pair of sequences $((b_n)_{n\geq 0}, (a_n)_{n\geq 1})$ in $k$, called sequence of partial denominators and sequence of partial numerators respectively.

## Also known as

A generalized continued fraction is also known as a general continued fraction.