Definition:Complete Quotient

Definition

Let $x$ be an irrational number.

The sequence of complete quotients is defined recursively by:

$\alpha_0 = x$

$\alpha_{n+1} = \displaystyle\frac1{\{\alpha_n\}}$

where $\{\cdot\}$ denotes fractional part.

Also see

• Definition:Sequence of Complete Quotients
• Definition:Sequence of Partial Quotients
• Definition:Convergent of Continued Fraction