Definition:Generalized Continued Fraction

Informal definition
Informally, a general continued fraction is a continued fraction in which the numerators can be any value, even functions in some contexts:


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

Definition
Let $k$ be a field.

A generalized continued fraction in $k$ is a pair of sequences $((b_n)_{n\geq 0}, (a_n)_{n\geq 1})$.

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

Also see

 * Definition:Regular Continued Fraction: a continued fraction in which the successive numerators are all $1$.