# Definition:Generalized Continued Fraction

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## Contents

## 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**.

## Also see

## Sources

- Weisstein, Eric W. "Generalized Continued Fraction." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/GeneralizedContinuedFraction.html