Definition:Generalized Continued Fraction

Definition
The form of continued fraction in which the successive numerators are all $1$ is called a regular continued fraction, or to be in canonical form.

If the numerators can be allowed to be any value, even functions in some contexts, the continued fraction is known as a general continued fraction:


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